Theresa bought a new desktop computer. One side of the desktop screen is 14 inches and the other side is 18 inches. What is the length of the diagonal of the desktop screen? Answer choices are rounded to the nearest inch. Ul 23 inches 20 inches 11 inches 16 inches

To find the length of the diagonal of the desktop screen, 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 desktop screen is 14 inches. - The other side of the desktop screen is 18 inches. Let's denote the length of the diagonal as \( d \). Using the Pythagorean theorem: \[ d^2 = 14^2 + 18^2 \] Now, we can calculate the length of the diagonal. Calculate the value by following steps: - step0: Calculate: \(14^{2}+18^{2}\) - step1: Evaluate the power: \(196+18^{2}\) - step2: Evaluate the power: \(196+324\) - step3: Add the numbers: \(520\) Calculate or simplify the expression \( \sqrt{520} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{520}\) - step1: Write as a product: \(\sqrt{4\times 130}\) - step2: Write in exponential form: \(\sqrt{2^{2}\times 130}\) - step3: Use the properties of radicals: \(\sqrt{2^{2}}\times \sqrt{130}\) - step4: Simplify the root: \(2\sqrt{130}\) The length of the diagonal of the desktop screen is approximately 22.8 inches. Therefore, the correct answer is 23 inches.