# The ratio of the lengths of the corresponding sides of similar triangles is 1.2

July 31, 2021 | education

| **The ratio of the lengths of the corresponding sides of similar triangles is 1.2, and the area of the larger triangle is 54 cm2, find the area of the small triangle.**

Since the triangles are similar, and the ratio of the lengths of the respective sides is 1.2, this is the coefficient of similarity of the triangles.

K = 1.2.

The ratio of the areas of similar triangles is equal to the square of the similarity coefficient.

S1 = 54 cm2.

S1 / S2 = K2.

54 / S2 = 1.44.

S2 = 54 / 1.44 = 37.5 cm2.

Answer: The area of the small triangle is 37.5 cm2.

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