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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.
Solution
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
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