Question

The two parallel sides of a trapezium and the distance between them are in the ratio 5 : 7 : 4. If the area of the trapezium is 216 $c{m}^2$, find its height.

• A. 4 cm
• B. 2 cm
• C. 5 cm
• D. 12 cm

Answer 1

The correct option is D 12 cm

We are given the ratio as,
5 : 7 : 4

Let the length of the two parallel lines be 5x (a) and 7x (b) and the distance between them as 3x (h).

$Area=\frac{1}{2}(a+b)\times h$ = $216c{m}^2$

$\to 216=\frac{1}{2}(5x+7x)\times 4x$

$\to 216=\frac{1}{2}(5x+7x)\times 4x$

$\to 24x^2=216$

$\to x^2=9$

$\to x=3$

Height, the disdance between the two parallel sides = 4x = $4\times 3$ = 12 cm