A triangle has sides with lengths of 24 inches, 45 inches, and 51 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 51 inches.

Step 2: Square the lengths of all sides: 24^2 = 576 45^2 = 2025 51^2 = 2601

Step 3: Check if the square of the longest side is equal to the sum of the squares of the other two sides: 2601 = 576 + 2025 2601 = 2601

Since the equation is true, the triangle is a right triangle.