# Triangles ABC and similar. ABC perimeter = 16 cm, perimeter = 48 cm. Find the ratio of the areas of the triangles.

March 27, 2021 | education

| Let’s designate the second triangle А1В1С1. Perimeter is the sum of the sides, the ratio of the perimeters will be equal to the coefficient of similarity. Find the coefficient of similarity.

R ABC / R A1B1C1 = 16/48 = 1/3.

One of the properties of such triangles is that the area ratio is equal to the square of the similarity coefficient.

We get:

S ABC / S A1B1C1 = (1/3) ² = 1/9.

Answer: The area ratio is 1/9.

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