Geometry

Question Analysis

The main focus is to utilize the Pythagorean Theorem Converse to ascertain if the corners of the window opening are right - angled. We must verify if the sum of the squares of the two adjacent sides of the window opening (functioning as the legs of a potential right - triangle) is equivalent to the square of the diagonal of the window opening (serving as 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 the context of the window opening, if the triangle formed by the two adjacent sides and the diagonal satisfies this equation, the window opening has right - angled corners.

Step - by - Step Solution

1. Identify the sides:

Let feet and feet be the adjacent sides of the window opening, and feet be the diagonal.

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate :

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