What is the hypotenuse length of a 12” x 12” square in roofing calculations?

To determine the length of the hypotenuse of a square with each side measuring 12 inches, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

For a square, the two sides can both be considered as 12 inches. Therefore, the calculation using the Pythagorean theorem is as follows:

1. Square the lengths of the sides: (12^2 + 12^2 = 144 + 144 = 288).

2. To find the length of the hypotenuse (c), take the square root of the sum of the squares: (c = \sqrt{288}).

Calculating the square root gives:

[

\sqrt{288} = \sqrt{144 \times 2} = 12\sqrt{2} \approx 12 \times 1.414 = 16.97.

]

Thus, the hypotenuse length of a 12” x 12” square is approximately 16.97 inches. This matches perfectly with the provided option that represents the correct length. Understanding the