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.
Let the length of the pasture be 20 yards and the width be 40 yards.
Using the Pythagorean Theorem, the length of the diagonal (d) can be calculated as:
d^2 = 20^2 + 40^2
d^2 = 400 + 1600
d^2 = 2000
d = sqrt(2000)
d = sqrt(500 * 4)
d = sqrt(500) * sqrt(4)
d = 10sqrt(5)
Therefore, the length of the diagonal pass with the mower is 10√5 yards.