Find the perimeters of similar triangles ABC and A1B1C1 if AB = 12 A1B1 = 3 AC = 16 B1C1 = 2.

univerkov | September 30, 2021 | education

If the triangles are similar, then their respective sides are proportional. Let us find the coefficient of similarity using the ratio of the sides AB and A1B1.

AB: A1B1 = 12: 3 = 4.

This means that each side of triangle ABC is 4 times larger than the corresponding side of triangle A1B1C1.

Let’s find the unknown sides of both triangles.

BC = B1C1 * 4 = 2 * 4 = 8.

A1C1 = AC: 4 = 16: 4 = 4.

The perimeter of triangle ABC is 12 + 8 + 16 = 36.

The perimeter of triangle A1B1C1 is 3 + 2 + 4 = 9, or 36: 4 = 9.

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