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Syllabus

1. InΔPQR, given that S is a point on PQ such that STIIQR and PS/SQ=3/5 If PR = 5.6 cm, then find PT.

2. InΔABC, AE is the external bisector of <A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.

3. P and Q are points on sides AB and AC respectively, ofΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

4. The image of a tree on the film of a camera is of length 35 mm,the distancefrom the lens to the film is 42 mm andthe distancefrom the lens to the tree is 6 m. How tall is the portion of the tree being photographed?

5. D is the midpoint of the side BC ofΔABC. If P and Q are points on AB and on AC such that DP bisects <BDA and DQ bisects <ADC, then prove that PQ II BC.

6. If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides thetwo sidesin the same ratio.

7. If a straight line divides anytwo sidesof a triangle in the same ratio, then the line must be parallel to the third side.

8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of <BAC and <DAC respectively, then prove that EF II BD. In aΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and <ADE = <DEA. Prove thatΔABC is isosceles.

9. In aΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.

10. The internal bisector of <A ofΔABC meets BC at D and the external bisector of <A meets BC produced at E. Prove that BD/ BE = CD/CE

11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.

12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 maway fromthe mirror, andthe distanceof his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).

13. In a rightΔABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that

(I) 9AQ

^{2}= 9AC^{2}+4BC^{2 }(II) 9 BP^{2}= 9 BC^{2}+ 4AC^{2}(III) 9 (AQ^{2}+BP^{2}) = 13AB^{2}14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and dividesΔABC into two parts equal in area. Find BP: AB.

15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ

^{2}+BP^{2}) = 5 AB^{2}16. In an equilateralΔABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2

17. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians ofthe triangle.

18. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^CB Prove that

1.AC

^{2}=AB^{2}+ BC^{2}+2 BC x BD19. Prove that in any triangle the sum of the squares of anytwo sidesis equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.

[To prove AB

^{2}+ AC^{2}= 2AD^{2}+ 2(1/2BC)^{2}]20. ABC is a right triangle right-angled at C and AC= √3 BC. Prove that <ABC=60

^{o}In Triangle ABC ,Angle B=90 and BD perpendicular AC, if AC=9 cm and AD=3 cm then BD is equal to

1. 2√2 cm

2.3√2 cm

3. 2√3 cm

4. 3√3cm

Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB

drawing boundaries PQ and RS which are parallel to BC.

Other measurements are as shown in the figure.

i. What is the area of this land?

ii. What is the length of PQ?

iii. The length of RS is

iv. Area of? APQ is?

v. What is the area of? ARS?

in triangle ABC,if AD is perpendicular to BCand AD*2=BD.DC,prove that angle BAC=90 degree

Q14. In the given figure, 3SR = 2SP ,ST || PM and ar ( $\u2206$PMR) = 50 cm

^{2}. Calculate.(a) ar ($\u2206$RST ) (b) ar ($\square $PMTS)

Proof of the theorem: ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

In the figure, XY is parallel to QR and PX/XQ= PY/YR = 1/2, then :(a) XY=QR

(b) XY=1/3 QR

(c) XY

^{2}= QR^{2}(d) XY = 1/2 QR

through the midpoint m of the side cd of a paralelogram abcd,the line bm is drawn intersecting ac in l and ad produced in e.prove that el=2bl

There is a triangular park ABC in a colony . The resident of Welfare

Association colony wishes to divide this park into two parts - one for plantingtrees and raising a lawn and the other for providing place for children to play. Theydecided to divide the park by creating a boundary along XY which is parallel to ACsuch that ar( BXY) = 2ar(ACYX). Statehow this boundary XYcan be drawnso that X and Y lie on AB and BC respectively??Prove that the ratio of areas of two similar triangles is equal to the square of their corresponding sides.

shape as the object but a different size. The scale of a drawing is a comparison of the length

used on a drawing to the length it represents. The scale is written as a ratio.

SIMILAR FIGURES: The ratio of two corresponding sides in similar figures is called the scale

Hence, two shapes are Similar when one can become the other after a resize, flip, slide, or

turn.

i. A model of a boat is made on a scale of 1:4. The model is 120cm long. The full size of the

boat has a width of 60cm. What is the width of the scale model?

ii. What will affect the similarity of any two polygons?

a. They are flipped horizontally

b. They are dilated by a scale factor

c. They are translated down

d. They are not the mirror image of one another

iii. If two similar triangles have a scale factor of a: b. Which statement regarding the two

triangles is true?

a. The ratio of their perimeters is 3a: b

b. Their altitudes have a ratio a: b

c. Their medians have a ratio : b

d. Their angle bisectors have a ratio a2

: b 2

The shadow of a stick 5m long is 2m. At the same time, the shadow of a tree 12.5m high is

v. Below you see a student's mathematical model of a farmhouse roof with measurements. The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges ofarectangularprism,EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have a length of 12 m. What is the length of EF, where EF is one of the horizontal edges of the block?

ABC is a right triangle, right angled at C. Let BC=a, CA=b, AB=c and let p be length of perpendicular from C on AB. Prove that

(i) cp=ab

(ii) 1/p

^{2}=1/a^{2}+1/b^{2}answer as quick as possible, tomorrow is my SA- 1 exam.

EXPERTS PLEASE GIVE A DETAILED ANSWER FOR THE ABOVE QUESTION. EXPLAIN EACH STEP

prove that in a right triangle the square of the hypotenuse is equal to the aum of the squares of the other two sides

In triangle PQR, ST || qr, PQ=6 cm, PR = 9 cm and PS = 2 cm. Find PTIn a triangle ABC, D and E are points on sides AB and AC respectively , such that DE is parallel to BC.If AD = 2.4cm, AE= 3.2cm , DE = 2cm and BC = 5cm , find BD and CE.

(a) 7.5cm

(b) 3cm

(c) 4.5cm

(d) 6cm

In a trapezium ABCD, AB is parallel to DC and DC = 2AB E is point on BC such that BE : EC = 3:4. EF is drawn parallel to AB where F is a point on AD . Prove that 7EF = 10AB.

triangle ABC is right angled at B. on the side AC, a point D is taken such that AD = DC and AB = BD. find the measure of angle CAB.

triangle ABC is right angled triangle at B.side BC is trisected at points D and E.Prove that 8AE

^{2}=3AC^{2}+5AD^{2}to his mind while making the kite. Give answers to his questions by looking at the figure.

Rahul tied the sticks at what angles to each other?

ii. Which is the correct similarity criteria applicable for smaller triangles at the upper part of

this kite??

iii. Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles

are in the ratio

iv. In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called:

?

v. What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?

in a right triangle ABC , right angled at C; P and Q are points of the sides AC and BC respectively , which divides these sides in the ratio 2:1. prove that :

(a)9(AO)2=9(AC)2 + 4(BC)2

(b)9(BP)2 =9(BC)2 + 4(AC)2

(c)9[(AO)2 + (BP)2] = 13(AB)2

in an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. prove that 9 AD

^{2 }= 7 AB^{2}in the figure of triangle ABC,d divides ca in the ratio of 4:3 .if DE// BC,then find the area of BCDE:are of triangle ABC.(diagram is not provided)

If O is any point inside a rectangle ABCD, then prove that OA

^{2}+ OC^{2}= OB^{2}+ OD^{2}Prove that the sum of squares of a sides of a rhombus is equal to the sum of the squares of its diagonals......pls give answer.....u'll surely get a ''thumbs up''

In a triangle ABC, AB=AC. D is any point on BC. Show that AB

^{2}-AD^{}^{2}^{}=^{BD.CD}1. Show that the area of a rhombus on hypotenuse of a right angled triangle, with one of the angles as 60 is equal to the sum of areas of rhombuses with one of their angles as 60 drawn on others sides.

2. BO and CO bisect angle B and angle C of triangle ABC. AO produced meets BC at P. Show:-

· AB*OP=BP*AO

· AC*OP=CP*AO

· AB*PC=AC*BP

· AP bisects angle BAC.

side ab and ac and median ad of a triangle abc r respectively proportional to sides pq and pr and median pm of another triangle pqr prove that triangle abc similar to pqr explain step by step it plz

the original kite. In original kite AO=BO=OF=OE=8cm. Triangle ABF is made of red colour

paper while other Triangle AEF is made of Yellow colour paper. On the basis of the information

and properties of geometrical figure answer the following questions.

(A). Identify Angle AOB?

(i) Right Angle

(ii) Obtuse Angle

(iii) Acute Angle

(iv) Scalene Triangle

(B). If AO:HN=2:1 and OB:NI =2:1 then what should be AB:HI , so that triangle AOB is similar

to triangle HNI ?

(i) 1:2

(ii) 4:1

(iii) 1:4

(iv) 2:1

(C). What is length of HI?

(i) 4√2 cm

(ii) 8√2 cm

(iii) 2√2 cm

(iv) None of these

(D).Calculate the area of triangle HMI if area of triangle ABE is 64 sq cm?

(i) 16 sq cm

(ii) 32 sq cm

(iii) 8 sq cm

(iv) 64 sq cm

(E). In a triangle, if the square of one side is equal to the sum of the squares of the other two

sides, then the angle opposite to the first side is a right angle. This theorem is called -

(i) Pythagoras theorem

(ii) Thales theorem

(iii) Converse of Thales theorem

(iv) Converse of Pythagoras theorem

Two poles of height "a" m. and "b"m. are "p" m apart. Proove that the point of intersection of lines joining the tops of the poles to bottom of the opp. poles is given by :- h = (a * b) / (a+b) m

PLZ. ANSWER EVEN A WEEK PASSED BUT NO ANS. FROM MERITNATION

In the figure ABCD is a parallelogram and E divides BC in the ratio 1:3. DB and AE intersect at F. Show that DF=4FB and AF=4FE.ABC & BDE R THE 2 EQUILATERAL TRIANGLES SUCH THAT D IS THE MID POINT OF BC .RATIO OF THE AREAS OF TRIANGLES ABC & BDE

In a triangle PQR,PR^2-PQ^2 and M is a point on side PR such that QM is perpendicular to PR.Prove that QM^2=PM*MR

If BL and CM are medians of a triangle ABC right angled at A, then prove that 4( BL

^{2}+ CM^{2}) = 5 BC^{2}The medians of a right angle triangle which are drawn from the vertices of the acute angles are 5 cm and 2 √10 cm. What is the length of the hypotenuse?

I am getting the answer as √13cm , but, I am still doubtful about the answer, so , I just wanted to confirm.

In triangle ABC, DE is parallel to BC and AD:DB=5:4. diagonals DC and BE intersect at F. Find Area(triangle DEF) / Area(triangle CFB).

in the given figure angle A=90 degree,AD perpendicular BC.If BD=2cm and CD=8cm,find AD

In triangle ABC, AD is a median . Prove that AB

^{2}+ AC^{2}= 2(AD^{2}+ BD^{2})In a quadrilateral ABCD, Angle B=90 degree, AD

^{2}=AB^{2}+BC^{2}+CD^{2}.Prove that Angle ACD=90 degree.

(i)Which among the following figures are congruent?(a) A and C (b) E and F (c) D and F (d) B and F(ii)If a line divides any two sides of the triangle in the same ratio, then the line is parallel to the third side. The statement depicts which theorem?(a) Pythagoras theorem ( b) Thales Theorem(c) Converse of Thales theorem (d) Converse of Pythagoras theorem(iii)Which of the following option is correct?(a) All similar figures are congruent(b) All congruent figures are similar(c) Similar figures have same size and shape.(d) None of these(iv)The height of the tree, when its shadow is 84 m long and at the same time a girl 2m high standing in the same straight line casts a shadow 12 m isd) none of these.(v)Using the concept of similarity ,the height of the tree isprove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides

II RS and MP/PR=2/3.If MS = 4.5 cm find MQ.

If A be the area of a right triangle and b one of the sides containing the right angle, the length of the altitude on the hypotenuse is__________.

a) 2A/√(b

^{2}+2A^{2}) b) 2Ab/√(b^{4}+4A^{2}) c)2Ab^{2}/√(b^{3}+4A^{2}) d)2A^{2}b/√(b^{4}+3A^{2})Triangle PQR~ Triangle XYZ If PQ=4cm,QR=5cmand XY=6cm. Then find YZ.

In triangle ABC if AD is the median then show that AB

^{2}+ AC^{2}= 2(AD^{2}+ BD^{2})In the figure if CD = 17 m, BD = 8 m and AD = 4 m, then find the value of AC.

D is the midpoint of side BC of a triangle ABC.AD is bisected at a point E and BE produced cuts AC at the point X.Prove that - BE : EX = 3:1

In an acute angled triangle ABC , AD is median in it,prove

4AD

^{2 }+BC^{2}=2AB^{2}+2AC^{2}In triangle ABC, angle A=60. Prove that BC

^{2}=AB^{2}+AC^{2}- AB.ACProve that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

CASE STUDYA beehive is an enclosed cell structure in which some honeybee species of the

subgenus Apis live and raise their young. Each cell is the form of hexagonal

shape. In a regular hexagon, there are six edges of equal lengths. Taking O as

centre, join all the vertices with the centre.

Similarity of Triangles

Two triangles are said to be similar if

- Corresponding angles are equal and

- Corresponding sides are proportional.

(i) Find the number of equilateral triangles in the corresponding figure.

(a) 6 (b) 4

(c) 3 (d) 8

(ii) If the areas of two equilateral triangles are equal, then these are always

(a) Similar

(b)Congruent

(c) Both similar and congruent

(d)None of these

(iii) How many triangles are similar in the given figure

(a) 6 (b) 4

(c) 3 (d) 8

(iv) Find the area of equilateral triangle if each edge is 4 units.

(a) 3 sq units (b) 6√3 sq units

(c ) 4√3 sq units (d) 5√3 sq units

(v) Find the area of hexagon, if each edge is 4 units.

(a) 18 sq units (b) 30√3 sq units

(c) 36√3 sq units (d) 24√3 sq units

If the diagonals of a quadrilateral divide each other proportionally , prove that itAskis a trapezium

^{2 }= QS* RS, then prove that PQR is right angles at PIN THE GIVEN FIGURE, DB IS PERPENDICULAR TO BC, DE IS PERPENDICULAR TO AB AND AC IS PERPENDICULAR TO BC. PROVE THAT BE/DE= AC/BC.i am a meritnation paid user

in equilateral trangle d is a pnt on bc side bd=1third bc prove that 9ad2 =7ab2

drawing boundaries PQ and RS which are parallel to BC.

Other measurements are as shown in the figure.

i. What is the area of this land?

ii. What is the length of PQ?

iii. The length of RS is

iv. Area of? APQ is?

v. What is the area of? ARS?

if AD is perpendicular to BC and BD=1/3 CD.prove that 2AC

^{2}=2AB^{2}+BC^{2}In a triangle ABC, angleB=90, AE=CD=13cm, BE=AD=5cm. Find BC

what is the difference between - median , altitude , perpendicular bisector and perpendicular - in a triangle?

please explain

In triangle ABC , AD is perpendicular to BC. Prove that AD

^{2}= 3DC....tried the question many tyms...cn sum1 pls explain with the steps.thankyou...

In an equilateral triangle ABC,D is a point on side BC such that 4BD = BC. prove that 16AD

^{2}= 13BC^{2}In a triangle ABC , AB =AC and D is a point on side AC , such that BC2=AC.CD . Prove that BD =BC . PLEASE HELP ME MERITNATION !!!

D is the midpoint of side BC of triangle ABC and E is midpoint of AD . BE produced meets AC at point M . Prove that BE=3EM

What are various aspects of pythagoras theorem?

In triangle PQR, a line XY parallel to QR cuts PQ at X and PR at Y in which PX/XQ=PY/YR=1/2.Then

a)XY=QR

b)XY=1/2QR

x+1/y= 1/zABC is an equilateral triangle. Find the ratio of the area of the equilateral triangle

described on a side of the triangle to the area of the equilateral triangle described on one ofits altitude.In the figure - PA,, QB and RC are perpendiculars to AC. prove that 1/x + 1/z = 1/y

In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that

(i) AB

^{2}= BC × BD(ii) AC

^{2}= BC × DC(iii) AD

^{2}= BD × CDhow to do this using pythagoras theorem ?

D is a point on the side BC of triangle ABC such that angle BAC= angle ADC. Prove that CA

^{2}= CB x CDIn triangle ABC points P,Q and R lie on sides BC, CA and AB respectively. If PQ||AB and QR||BC then prove that RP||CA

In given figure, is a right triangle PQR, right angled at Q. X and Y are the points on PQ and QR such that PX : XQ=

1 : 2 and QY : YR= 2 : 1. Prove that 9(PY2+XR2)=13PR2.Angle ABD=angle CDB=angle PQB=90.If AB=x units,CD=y units,PQ=z units prove that 1/x+1/y=1/z

In triangle ABC, P and Q are points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that medium AD, drawn from A to BC, bisects PQ.

ABCD is a rectangle in which BC = 2AB. a point E lies on ray CD such that CE = 2BC. prove that BE is perpendicular to AC.

Please explain the exterior angle bisector theorem!!!

ar of triangle AMN/ at of triangle ABC = --------

In the adjoining figure, ABCD is a trapezium in which CD||AB and its diagonals intersect at O. If AO=(5x-7)cm, OC=(2x+1)cm, DO=(7x-5)cm and OB=(7x+1)cm, find the value of x.

Experts, this question is from RS Aggarwal book (Class 10 Mathematics) and the same question's solution is also given on your website. But the values of OB and OD have been interchanged in your solution so the answer is coming right. But is that the correct way to do this question?? Please give the correct solution. Please answer fast, have to give an assignment tomorrow...

SAMPLE PAPER/MODEL TEST PAPERSUBJECT – MATH 10^{TH}CBSE SA 2 2011Section – A1. A number is selected from numbers 1 to 25. The probability that it is prime is:

(a) 5/6(b) 1/3(c) 1/6(d) 2/3

2. If the angle of elevation of the top of a tower from two points distance a and b from the base and in the same straight line with at are complementary, then the height of the tower is:

(a) a/b(b) ab(c) √ ab(d) √a/b

3. The perimeter of a triangle is 30 cm and the circumference of its in circle is 88 cm. Then area of triangle is:

(a) 420 cm

^{2}(b) 140 cm^{2}(c) 70 cm^{2}(d) 210 cm^{2}4. If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is:

(a) 2800(b) 16000(c) 3200(d) 200

5. The surface area of a sphere is same as the curved surface of right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:

(a)12 cm(b) 4 cm(c) 3 cm(d) 6 cm

6. If the circumference and the area of a circle are numerically equal, then diameter of the circle is:

(a) π/2(b) 2π(c) 2(d) 4

7. AB and CD are two common tangents of circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to:

(a)12cm(b) 6 cm(c) 4 cm(d) 8cm

8. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ= 12 cm. Length PQ is:

(a) 13 cm (b) 8.5 cm(c) √119(d) 12 cm

9. If three coins are tossed simultaneously, then the probability of getting at least two heads, is:

(a) ¼(b) ½(c) 2/4 (d) 3/8

10. The area of in circle of an equilateral triangle is 154 cm

^{2}.The perimeter of the triangle is:(a) 72.7 cm(b) 72.3 cm(c) 71.5 cm(d)71.7 cm

Section – B11. Prove that the tangents drawn at the ends of a diameter of a circle are paralled.

12.A bag contains 7 white, 4 red and 9 black balls. A ball is drawn at the random. What is the probability that ball drawn is not white?

13. Shoe that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

14. Using the quadratic formula, solve the equation:

A

^{2}b^{2}x^{2}– (4b^{4}– 3a^{4}) x – 12a^{2}b^{2}= 015. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

16. Find the radius of circle whose area is equal to the sum of the areas of three circles whose radii are 3 cm, 4 cm and 12cm.

17. The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q.

If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, find the values of p and q.

18. Find the area of a circular ring whose external and internal diameters are 20 cm and 6 cm.

Section – C19. If m times the m

^{th}tern of an A.P. is equal to n times its n^{th}term, find (m + n)^{th}term of A.P.?20.Two tangents TP and TQ are drawn from an external point T to a circle with centre O. As shown in fig. or if they are inclined to each other at an angle of 100

^{0}then what is the value of ∟POQ?21. From the top of house, h meters high from the ground, the angle of elevation and depression of the top and bottom of a tower on the other side of the street are ѳ and φ, respectively. Prove that the height of the tower h (1+ tan ѳ cot ѳ).

22. A motor boat whose speed is 8cm/hour in still water goes 15 km down stream and comes back in a total time of 3 hours 40 minutes. Find the speed of the stream.

23. For what value of n are the nth terms of two A.P. is 63, 65, 67 ……… and 3, 10, 17……… equal?

24. Construct a triangle ABC in which AB = 6.5 cm, ∟B = 60

^{0}and BC = 5.5 cm. Also construct a triangle ABC similar to triangle ABC, whose each side is 3/2 times the corresponding side of the triangle ABC.25. A bag contains 5 white balls, 7 red balls, 4 black balls and 2blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is:

(a) Not white

(b) Red or black

(c) White or blue

(d) Neither white not black

26. PQRS is a square land of the side 28 m. Two semicircular grass covered portions are to be made on two of its opposite sides as shown in the figure. How much area will be left uncovered? [Take π = 22/7]

27. A solid composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and radius of each hemispherical end is 7cm, find the cost of polishing its surface at the rate of Rs.10 per dm

^{2}28. If A (4,-8), B (3, 6) and C (5, -4) are the vertices of triangle ABC, D is the mid point of BC and P is a point on adjoined such that AP/PD = 2. Find the coordinate of P.

Section – D29. Solve for x:

X

^{4}+2x^{3}+ 13x^{2}+ 2x + 1 = 0.30. The angles of depression of the top and bottom of an8 m tall building from the top of a multistoreyed building are 30

^{0}and 45^{0}respectively. Find the height of the multi storeyed building and the distance between the two buildings.31. Solve for x:

2 (x

^{2}+ 1/x^{2}) – (x + 1/x) – 11 = 032. A class consists of a number of boys whose ages are in A.P., the common difference being 4 months. If they youngest boy is just eight years old and if sum of the ages is 168 years. Find the number of boys in the class.

33. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of first triangle.

34. A car has to wipers which do not over lap each wiper has a blade of length 25 cm sweeping through an angle 115

^{0 }. Find the total area cleared at each sweep of the blades.Two poles of height a and b metres are p metre apart . Prove that the height of each pole to the foot of opposite pole is given by ab/a+b metres.

ABC and DBC are two triangles on the same base BC.If AD intersects BC at O,show that ar(ABC)/ar(DBC)=AO/DO

IF THE AREAS OF TWO SIMILAR TRIANGLES ARE EQUAL,,PROVE THAT THEY ARE CONGRUENT...

in triangle ABC,ANGLE B=90, BC=5CM, AC-AB=1. EVALUATE 1+sinC/1+cosC