Find the ratio of the areas of two triangles if the sides of one are 5 cm, 8 cm, 12 cm, and the sides

univerkov | March 8, 2021 | education

Find the ratio of the areas of two triangles if the sides of one are 5 cm, 8 cm, 12 cm, and the sides of the other are 15 cm, 24 cm, 36 cm.

The lengths of the sides of the second triangle are three times the lengths of the sides of the first triangle, therefore, the sides of the triangles are proportional, and the triangles are similar in the third feature of similarity.

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

K = 5/15 = 8/24 = 12/36 = 1/3.

Then S2 / S2 = (1/3) 2 = 1/9.

Answer: The ratio of the areas of the triangles is 1/9.

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