Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine if the corners of the box face are right - angled. We need to check if the sum of the squares of the two adjacent sides of the box face (which would be the legs of a right - triangle) equals the square of the diagonal of the box face (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 box face, if the two adjacent sides and the diagonal form a right - triangle, then the box face has right - angled corners.

Step - by - Step Solution

1. Identify the sides:

Let  inches and  inches be the adjacent sides of the box face, and  inches be the diagonal of the box face.

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate :

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