A certain television is advertised as a 38 -inch TV (the diagonal length). If the height of the TV is 25 inches, how wide is the TV? Round to the nearest tenth of an inch.

To find the width of the TV, we can use the Pythagorean theorem since we have the diagonal length and the height of the TV. Given: - Diagonal length (d) = 38 inches - Height (h) = 25 inches We can use the Pythagorean theorem to find the width (w): \[ d^2 = h^2 + w^2 \] Substitute the given values: \[ 38^2 = 25^2 + w^2 \] Solve for w: \[ 1444 = 625 + w^2 \] \[ w^2 = 1444 - 625 \] \[ w^2 = 819 \] \[ w = \sqrt{819} \] Now, we can calculate the width of the TV by finding the square root of 819 and rounding it to the nearest tenth of an inch. Calculate the value by following steps: - step0: Calculate: \(\sqrt{819}\) - step1: Write as a product: \(\sqrt{9\times 91}\) - step2: Write in exponential form: \(\sqrt{3^{2}\times 91}\) - step3: Use the properties of radicals: \(\sqrt{3^{2}}\times \sqrt{91}\) - step4: Simplify the root: \(3\sqrt{91}\) The width of the TV is approximately 28.6 inches when rounded to the nearest tenth of an inch.