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Question

The area of a trapezium is 384 cm2. Its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them is 12 cm. Find the length of each one of the parallel sides.

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Solution

Given:Area of the trapezium = 384 cm2The parallel sides are in the ratio 3:5 and the perpendicular height between them is 12 cm.Suppose that the sides are in x multiples of each other.Then, length of the shorter side = 3x Length of the longer side = 5xArea of a trapezium=12×(Sum of parallel sides)×(Height)384=12×(3x+5x)×(12)384=122×(8x)384=6×(8x)8x=3846=64x=648=8 cmLength of the shorter side=3×x=3×8=24 cmAnd, length of the longer side=5×x=5×8=40 cm

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