Kirk has a yard that is 140 feet by 90 feet. How long would it be ithe measured from the top right to the bottomnert of his yard? Round to the nearesthundedths place.

To find the length of the diagonal of Kirk's yard, we can use the Pythagorean theorem, which 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: Length of the yard = 140 feet Width of the yard = 90 feet Let's denote: Length of the yard as \( l = 140 \) feet Width of the yard as \( w = 90 \) feet The length of the diagonal (\( d \)) can be calculated using the Pythagorean theorem: \[ d = \sqrt{l^2 + w^2} \] Substitute the given values: \[ d = \sqrt{140^2 + 90^2} \] Now, we can calculate the length of the diagonal. Calculate the value by following steps: - step0: Calculate: \(\sqrt{140^{2}+90^{2}}\) - step1: Add the numbers: \(\sqrt{27700}\) - step2: Write as a product: \(\sqrt{100\times 277}\) - step3: Write in exponential form: \(\sqrt{10^{2}\times 277}\) - step4: Use the properties of radicals: \(\sqrt{10^{2}}\times \sqrt{277}\) - step5: Simplify the root: \(10\sqrt{277}\) The length of the diagonal of Kirk's yard is approximately 166.43 feet when rounded to the nearest hundredths place.