A triangle has sides with lengths of 24 inches, 45 inches, and 51 inches. Is it a right triangle? yes no

To determine if a triangle with sides of lengths 24 inches, 45 inches, and 51 inches is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. Let's denote the sides as follows: - \( a = 24 \) - \( b = 45 \) - \( c = 51 \) (the longest side) We need to check if: \[ c^2 = a^2 + b^2 \] Now, let's calculate \( c^2 \) and \( a^2 + b^2 \): 1. Calculate \( c^2 \): \[ c^2 = 51^2 \] 2. Calculate \( a^2 + b^2 \): \[ a^2 + b^2 = 24^2 + 45^2 \] Now, I will perform these calculations. Calculate the value by following steps: - step0: Calculate: \(51^{2}\) - step1: Evaluate the power: \(2601\) Calculate or simplify the expression \( 24^2 + 45^2 \). Calculate the value by following steps: - step0: Calculate: \(24^{2}+45^{2}\) - step1: Evaluate the power: \(576+45^{2}\) - step2: Evaluate the power: \(576+2025\) - step3: Add the numbers: \(2601\) The calculations yield the following results: 1. \( c^2 = 51^2 = 2601 \) 2. \( a^2 + b^2 = 24^2 + 45^2 = 2601 \) Since \( c^2 = a^2 + b^2 \), we have: \[ 2601 = 2601 \] This confirms that the triangle with sides of lengths 24 inches, 45 inches, and 51 inches is indeed a right triangle. **Final Answer:** Yes, it is a right triangle.