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

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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