Question

The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm², find x.

Answer 1

Area of a trapezium = `(1)/(2)`

(sum of parallel sides) x height

Lengths of parallel sides are (x + 9) and (2x – 3)

and height = (x + 4)

According to the condition,

`(1)/(2)(x + 9 + 2x - 3) xx (x + 4)` = 540

⇒ (3x + 6)(x + 4) = 540 × 2

⇒ 3x² + 12x + 6x + 24 - 1080 = 0

⇒ 3x² + 18x - 1056 = 0

⇒ x² + 6x - 352 = 0          ...(Dividing by 3)

⇒ x² + 22x - 16x - 352 = 0

⇒ x(x + 22) - 16(x + 22) = 0

⇒ (x + 22)(x - 16) = 0

Either x + 22 = 0,

then x = -22

But it is not possible as it is negative.

or

x - 16 = 0,

then x = 16