Question

The area of a trapezium is 459 cm${}^2$. Its parallel sides are in the ratio 7: 10 and the perpendicular distance between them is 9 cm. Find the length of each of the parallel sides.

Answer 1

Area of a trapezium = 459 cm${}^2$

The ratio of parallel sides of the trapezium = 7 : 10

The perpendicular distance between parallel sides = 9 cm

Let the common ratio be x,

Then, the parallel sides are 7x, 10x

The area of the trapezium formula is $\frac{1}{2}(a+b)h$

Area of trapezium = 459 cm${}^2$

$\frac{1}{2}(a+b)h=459$

$\frac{1}{2}(7x+10x)9=459$

$\frac{1}{2}\left(17x\right)9=459$

$153x=459\times 2$

$153x=918$

$x=6$

The parallel sides of the trapezium are 7 $\times$ 6 = 42 cm, 10 $\times$ 6 = 60 cm.

Therefore, the length of each parallel side is 42 cm, 60 cm.