A triangle has sides with lengths of 7 feet, 24 feet, and 25 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 7 feet and 24 feet as a and b, and the side of length 25 feet as c.

First, square the lengths of a and b:

7^2 = 49 24^2 = 576

Then, add these two numbers together:

49 + 576 = 625

Next, square the length of c:

25^2 = 625

Since the sum of the squares of a and b is equal to the square of c, this is a right triangle.