In the figure BC || DE, area of ΔABC = 25 sq. cm, area of trapezium BCED = 24 sq. cm and DE = 14 cm. Calculate the length of BC.

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Solution

Given: BC || DE, area (ΔABC) = 25 sq. cm, DE = 14 cm and area (trapezium BCED) = 24 sq. cm

From the figure, we have:

Area (ΔADE) = Area (ΔABC) + Area (trapezium BCED) = 25 + 24 = 49 sq. cm

Since BC || DE, ΔABC and ΔADE are similar.

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.

Hence, the length of BC is 10 cm.

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