Is it possible to construct a quadrilateral MIST in which MI=3.5 cm,ST=3.5 cm,TM=7.9 cm,MS=8.4 cm and IT =4.5 cm?Give reasons for your answer.please it is urgent for my exam.
Yes it is possible to construct the required quadrilateral of given dimensions.
In order to check whether the quadrilateral can be formed we use the property that 'Sum of two sides of triangle is always greater than the third side'.
In this case the above property is satisfied.
The following table may help you to see the possible measurements to draw a quadrilateral.
No | Number of sides | Number of diagonals | Number of angles | Total number of elements |
1 | 2 | 2 | 1 | 5 |
2 | 2 | 1 | 2 | 5 |
3 | 4 | 1 | - | 5 |
4 | 4 | - | 1 | 5 |
5 | 3 | - | 2(Included) | 5 |
6 | 3 | 2 | - | 5 |
7 | 2(adjacent) | - | 3 | 5 |
In this case you need to follow the following steps in order to carry out the required construction.
Step 1:Draw MT = 7.9 cm using scale.
Step 2: Taking M as centre draw an arc of 8.4 cm.
Step 3: Now taking T as centre draw an arc of 3.5 cm which intersects the arc drawn from M in order to get S and join TS.
Step 4: Taking T as centre again draw an arc of 4.5cm.
Step 5: Now taking M as centre and arc of radius 3.5cm which intersect the previous arc to get the point I.
Step 6: Join IS and IM in order to get the required quadrilateral MIST.
