The length of the diagonal can be found using the Pythagorean Theorem:
diagonal^2 = 20^2 + 40^2
diagonal^2 = 400 + 1600
diagonal^2 = 2000
Taking the square root of both sides:
diagonal = √2000
diagonal = √(100 * 20)
diagonal = 10√20
diagonal = 10√4*5
diagonal = 10 * 2√5
diagonal = 20√5
Therefore, the length of the diagonal pass with the mower is 20√5 yards.
Question A gardener is mowing a 20 by 40 yard rectangular pasture using a diagonal pattern. He mows from one corner of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form. Recall from the Pythagorean Theorem that, for a right triangle, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. (1 point) Responses Image with alt text: 10 times square root 20 Image with alt text: 20 times square root 2 Image with alt text: 400 times square root 5
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