Geometry

Question Analysis

This question is centered around the concept of Ratio in Similar Shapes. The main focus is on applying the principle that corresponding sides of similar triangles are in proportion. Given the lengths of two sides of one triangle and one side of a similar triangle, we need to find the missing side length by establishing and solving a proportion.

Key Concept Explanation

In similar triangles, the key concept is that the ratios of corresponding side lengths are equal. This fundamental property allows us to create an equation (a proportion) to solve for unknown side lengths. By matching up the corresponding sides correctly, we can use cross - multiplication and basic algebraic operations to find the value of the missing side.

Step - by - Step Solution

1. Set up the proportion:

Since the triangles are similar and 1.5 corresponds to 9 and 2.7 corresponds to , we set up the proportion .

2. Cross - multiply:

Cross - multiplying gives us .

3. Calculate the right - hand side:

First, find . So the equation becomes

Click "Show Answer" to reveal the answer and analysis