A triangle has sides with lengths of 33 inches, 55 inches, and 66 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.

Step 1: Identify the longest side. In this case, the longest side is 66 inches.

Step 2: Square the lengths of all sides: 33^2 = 1089 55^2 = 3025 66^2 = 4356

Step 3: Check if the square of the longest side is equal to the sum of the squares of the other two sides: 1089 + 3025 = 4114

Since 4114 is not equal to 4356, this triangle is not a right triangle.