The areas of such triangles are 35 cm2 and 315 cm2. One of the sides of the first triangle is 14 cm.

| February 13, 2021 | education

The areas of such triangles are 35 cm2 and 315 cm2. One of the sides of the first triangle is 14 cm. Find the side of the second triangle and the ratio of the perimeters of the triangles.

It is known that the ratio of the lengths of similar sides of similar triangles is equal to the coefficient of similarity, and the ratio of the areas of similar triangles is equal to the square of the coefficient of similarity. Knowing the areas of such triangles, we find the similarity coefficient:

k ^ 2 = S2 / S1 = 315/35 = 9;

k = √9 = 3.

The sums of the lengths of similar triangles are the same as the lengths of their sides. Therefore, the ratio of the perimeters of these triangles is 3.

The length of the side of the second triangle, which is similar to the side of the first triangle, equal to 14 cm, is 14 * 3 = 42 cm.



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