# The difference between the two parallel sides of a trapezium is 8 m. The perpendicular distance between them is 24 m.

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The difference between the two parallel sides of a trapezium is 8 m. The perpendicular distance between them is 24 m. If the area of the trapezium is 312 m2, then what are the lengths of the two parallel sides ?

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Let x and x + 8 be the two parallel sides of the trapezium. Then,

$\frac{1}{2}\times(x +x+8)$ x 24 = 312 ⇒ 2x + 8 = 26 ⇒ 2x = 18 ⇒ x = 9

∴ The two parallel sides are 9 m and 17 m.