A triangle has sides with lengths of 16 feet, 63 feet, and 65 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 16 feet and 63 feet as a and b, and the side of length 65 feet as c.

First, we square the lengths of a and b:

16^2 = 256 63^2 = 3969

Then we add these two numbers together:

256 + 3969 = 4225

Next, we square the length of c:

65^2 = 4225

Since the sum of the squares of a and b is equal to the square of c, we can conclude that the triangle is a right triangle.