The triangles above are similar. What is the ratio larger smaller of the perimeters?

Answer 1

Since the triangles are similar, their corresponding sides are in proportion to each other. Let's denote the ratio of the larger triangle's perimeter to the smaller triangle's perimeter as x.

By the property of similar triangles, the ratio of their sides is the same as the ratio of their perimeters. Therefore, we have:

Perimeter(Larger triangle) / Perimeter(Smaller triangle) = x

Let's denote the side lengths of the larger triangle as L1, L2, and L3, and the side lengths of the smaller triangle as S1, S2, and S3.

Then, we have:

L1 / S1 = L2 / S2 = L3 / S3 = x

Now, the perimeter of a triangle is the sum of its sides. Therefore:

Perimeter(Larger triangle) = L1 + L2 + L3
Perimeter(Smaller triangle) = S1 + S2 + S3

Given that L1 / S1 = L2 / S2 = L3 / S3 = x, we can rewrite the perimeters in terms of x:

Perimeter(Larger triangle) = x * Perimeter(Smaller triangle)

So, the ratio of the larger triangle's perimeter to the smaller triangle's perimeter is x.