A triangle has sides with lengths of 15 inches, 18 inches, and 20 inches. 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 20-inch side to be the hypotenuse, since it is the longest side. So, we can plug the lengths of the sides into the Pythagorean theorem:

15^2 + 18^2 = 20^2 225 + 324 = 400 549 = 400

Since 549 does not equal 400, this triangle is not a right triangle according to the Pythagorean theorem.