What is the length of the hypotenuse if both other sides of a right triangle measure 12 feet and 16 feet?

To find the length of the hypotenuse in a right triangle when the lengths of the other two sides are known, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, if one side measures 12 feet and the other side measures 16 feet, you would calculate the hypotenuse (c) as follows:

1. Square both side lengths:

• ( 12^2 = 144 )

• ( 16^2 = 256 )

2. Add these two values together:

• ( 144 + 256 = 400 )

3. Finally, take the square root of the sum to find the hypotenuse:

• ( c = \sqrt{400} = 20 ) feet.

This confirms that the length of the hypotenuse is indeed 20 feet. This is why the correct answer represents the appropriate calculation using the foundational geometry principles applied to a right triangle.