Question

The parallel sides of an isosceles trapezium are in the ratio $2:3$. If its height is $8cm$ and area is $240c{m}^2$, then its perimeter is ____ cm.

• A. 96
• B. 100
• C. 60
• D. 80

Answer 1

The correct option is D

80

Let the parallel sides AB and DC be $2x$ and $3x$ respectively.

Area = $\frac{1}{2}(2x+3x)h$

$240=\frac{1}{2}\left(5x\right)\times 8$

$x=12$

$\therefore AB=2\left(12\right)=24cm$

$DC=3\left(12\right)=36cm$

We know $EC=\frac{36-24}{2}=\frac{12}{2}=6cm$

In $△BEC,BC=10cm$ $(3-4-5PythagorasTriplet)$

Hence perimeter of trapezium = $24+10+36+10$

$=80cm$