Solve the 17th question.
17. The sides (other than hypotenuse) of a right triangle are in the ratio 3:4. A rectangle is described on its hypotenuse,the hypotenuse being the longer side of the rectangle.The breadth of the rectangle is four-fifth of its length.Find the shortest side of the right triangle,if the perimeter of the rectangle is 180cm.‚Äč
[ Hint :   Hypotenuse = sum   of   sqaures   of   sides = 3 x 2 + ( 4 x ) 2 = 25 x 2 = 5 x Breadth   of   the   rectangle = 4 5 5 x = 4 x ]

 

Dear Student,
Here is the solution of your asked query:

Given  : The sides (other than hypotenuse) of a right angled triangle are in the ratio 3 : 4.

Let ratio coefficient  =  x 
So,
Sides  =  3x  and 4x

We know :

Hypotenuse 2 =  Adjacent 2 + Opposite 2

Hypotenuse 2 =  ( 3x )2 + ( 4x )2

Hypotenuse 2 =  9x 2 + 16 x 2

Hypotenuse 2 =  25 x 2

Hypotenuse 2 =  ( 5x ) 2

Hypotenuse =   5x  

As given : The hypotenuse being the longer side of the rectangle. The breadth of the rectangle in four-fifth of its length.
So,

Length of rectangle  = 5 x

And

Breadth  = 5x × 45 = 4x 

We know perimeter of rectangle  =  2 ( Length  + Breadth )

Given : The perimeter of the rectangle is 180 cm , So

2 ( 5x  + 4x ) =  180

2 ( 9x ) =  180

18 x  =  180

x  =  10 

So,

Sides of triangle  =  3 ( 10 ) =  30 cm , 4 ( 10 ) = 40 cm and  Hypotenuse 5 ( 10 ) =  50 cm

Shortest side of right angle triangle  =  30 cm      

Regards                                                    

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I need it now.
  • -1
Let the speeds= s + s' + 5
425=(2s+5) x 5
425= 10s + 25
10s = 400
s = 40
s + 5= 45
Their average speeds are 40 km/hr and 45 km/hr
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