Geometry

Question Analysis

This question involves Ratio in Similar Shapes. The main focus is on using the proportional relationship between the height and shadow length of similar objects (the monument and the statue) to find the unknown height of the statue. Since the monument and the statue are in the same lighting conditions, the triangles formed by the objects, their shadows, and the lines of light are similar, and their corresponding sides are in proportion.

Key Concept Explanation:

The key concept here is the property of similar triangles. In similar triangles, the ratios of corresponding sides are equal. For the monument and the statue, the ratio of the height of the monument to the length of its shadow is the same as the ratio of the height of the statue to the length of its shadow.

Step-by-Step Solution

1. First, find the ratio of the height of the monument to the length of its shadow. The height of the monument is 40 feet and the length of its shadow is 32 feet. So the ratio is .

2. Let the height of the statue be feet. Since the ratios are equal for similar triangles, we can set up the proportion .

3. Cross - multiply to solve for . We get