A triangle has sides with lengths of 63 feet, 65 feet, and 16 feet. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which 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. This is often written as a^2 + b^2 = c^2.

In this case, we can consider the sides of lengths 63 feet and 16 feet as a and b, and the side of length 65 feet as c (the hypotenuse).

So, we calculate:

a^2 + b^2 = c^2 63^2 + 16^2 = 65^2 3969 + 256 = 4225

Adding 3969 and 256 gives us 4225, which is indeed equal to 65^2.

Therefore, the triangle with sides of 63 feet, 65 feet, and 16 feet is a right triangle.