# The area of a field in the shape of a trapezium measures 1440 m^2 . The perpendicular distance between its parallel sides is 24 m.

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The area of a field in the shape of a trapezium measures 1440 m2 . The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, what is the length of the longer parallel side ?

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Let the parallel sides be 5x and 3x respectively.

Then, $\frac{1}{2}\times$ 24 x (5x + 3x) = 1440 ⇒ 8x = $\frac{1440\times2}{24}$ ⇒ x = 15 m.

∴ The longer parallel side = 5 × 15 m = 75 m.