What is the length of the diagonal of a rectangle with a width of 3 inches and a height of 4 inches?

To find the length of the diagonal of a rectangle, the Pythagorean theorem is utilized. This theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in the case of the rectangle) is equal to the sum of the squares of the lengths of the other two sides (the width and height).

In this case, the rectangle has a width of 3 inches and a height of 4 inches. Using the Pythagorean theorem, the length of the diagonal can be calculated as follows:

1. Square the width: (3^2 = 9).

2. Square the height: (4^2 = 16).

3. Add these two results together: (9 + 16 = 25).

4. Take the square root of the sum to find the length of the diagonal: (\sqrt{25} = 5).

Therefore, the length of the diagonal is 5 inches, making this the correct answer. This direct application of the Pythagorean theorem demonstrates its practical use in determining dimensions in aviation maintenance and other fields involving measurements.