Question

The area of a trapezium is 91 cm² and its height is 7 cm. If one of the parallel sides is longer than the other by 8 cm, find the two parallel sides.

Answer 1

Given that,

Let the length of one parallel side of the trapezium = x meter

Length of other parallel side of trapezium = (x + 8) meter

Area of trapezium = 91 cm²

Height = 7 cm

We know that,

Area of trapezium = `1/2("Sum of lengths of parallel sides") xx "altitude"`

`91 = 1/2(x + x + 8) xx 7`

91 = `1/2(2x + 8) xx 7`

91 = (x + 4) × 7

(x + 4) = `91/7`

x + 4 = 13

x = 13 - 4

x = 9

∴  Length of one parallel side of trapezium = 9 cm

And, Length of other parallel side of trapezium = x + 8 = 9 + 8 = 17 cm