Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to check if the lengths of the planks can form a right - triangle. We need to verify if the sum of the squares of the two shorter lengths equals the square of the longest length.

Key Concept Explanation

The Pythagorean Theorem Converse states that for a triangle with side lengths , , and (where is the longest side), if , then the triangle is a right - triangle.

Step - by - Step Solution

1. Identify the sides:

The lengths of the planks are 12 feet, 16 feet, and 20 feet. The longest side feet, and the two shorter sides are feet and feet.

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate

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