Question

The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 575 cm${}^2$, find the length of the parallel sides.

Answer 1

The ratio of parallel sides of the trapezium = 10: 13.

Distance between them = 25 cm

Area of trapezium = 575 cm${}^2$

Let the common ratio be 𝑥,

Then, the parallel sides are 10x, 13x

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

Area of trapezium = 575 cm${}^2$

$\frac{1}{2}(10x+13x)25=575$

$23x\times 25=575\times 2$

$575x=1310$

$x=2$

the parallel sides of the trapezium are 10 $\times$ 2 = 20 cm , 13 $\times$ 2 = 26 cm