Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine if the corners of the rectangular pen are right - angled. We need to check if the sum of the squares of the two adjacent sides (which would be the legs of a right - triangle formed in the rectangle) equals the square of the diagonal (the hypotenuse of the right - triangle).

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. In a rectangle, if we consider two adjacent sides and the diagonal, they form a right - triangle if the rectangle has right - angled corners.

Step - by - Step Solution

1. Identify the sides:

Let feet and feet be the adjacent sides of the rectangle, and feet be the diagonal.

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate

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