Geometry

Question Analysis

This question focuses on the Perimeters of Similar Shapes. The main task is to determine the ratio of the perimeters of two similar triangles by using the ratio of their corresponding side lengths.

Key Concept Explanation

For similar triangles, the ratio of perimeters is equal to the ratio of their corresponding side lengths. This is because perimeter is a linear measurement, and similar triangles maintain a consistent proportionality for all linear dimensions.

Step - by - Step Solution

1. First, identify a pair of corresponding sides. Let's take the side of length  in the left triangle and the side of length  in the right triangle.

2. Calculate the ratio of the corresponding side lengths: .

We can also check with another pair. If we take the side of length  in the left triangle and assume the corresponding side in the right triangle is . Since the triangles are similar, using the ratio , we have

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