Geometry

Question Analysis

This question focuses on the Perimeters of Similar Shapes. The core is to use the property that for similar triangles, the ratio of perimeters is the same as the ratio of corresponding side lengths to find the required ratio.

Key Concept Explanation

For similar triangles, if the scale factor (ratio of corresponding side lengths) is , then the ratio of their perimeters is also . This is because the perimeter is a linear measurement, and similar triangles maintain a consistent proportionality for all linear aspects.

Step - by - Step Solution

1. Identify corresponding sides. Let's take two corresponding sides, say the side of length  in the left triangle and the side of length  in the right triangle.

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