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.%0D%0A%0D%0ARecall 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.
Let's label the sides of the rectangle as follows:
Side 1: 20 yards
Side 2: 40 yards
According to the Pythagorean Theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. Therefore, we have:
Diagonal^2 = Side 1^2 + Side 2^2
Diagonal^2 = 20^2 + 40^2
Diagonal^2 = 400 + 1600
Diagonal^2 = 2000
To find the length of the diagonal, we take the square root of both sides:
Diagonal = √2000
Simplifying this square root, we find:
Diagonal ≈ 44.72 yards
Therefore, the length of the diagonal pass with the mower is approximately 44.72 yards.