Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? Answer choices are rounded to the nearest inch 48 inches 34 inches 68 inches 23 inches

To find the length of the diagonal of the mirror, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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. Given: - One side of the mirror is 38 inches. - The other side of the mirror is 30 inches. Let's denote the length of the diagonal as \( d \). Using the Pythagorean theorem: \[ d^2 = 38^2 + 30^2 \] Now, we can calculate the length of the diagonal. Calculate the value by following steps: - step0: Calculate: \(38^{2}+30^{2}\) - step1: Evaluate the power: \(1444+30^{2}\) - step2: Evaluate the power: \(1444+900\) - step3: Add the numbers: \(2344\) Calculate or simplify the expression \( \sqrt{2344} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{2344}\) - step1: Write as a product: \(\sqrt{4\times 586}\) - step2: Write in exponential form: \(\sqrt{2^{2}\times 586}\) - step3: Use the properties of radicals: \(\sqrt{2^{2}}\times \sqrt{586}\) - step4: Simplify the root: \(2\sqrt{586}\) The length of the diagonal of the mirror is approximately 48 inches. Therefore, the correct answer is 48 inches.