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)

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)

A: 10√20
B: 20√2
C: 400√5
D: 20√5

Answer 1

C: 400√5

To find the length of the diagonal, we can use the Pythagorean Theorem. The two sides of the rectangle are 20 yards and 40 yards, so the diagonal (d) can be found using the formula:

d^2 = 20^2 + 40^2
d^2 = 400 + 1600
d^2 = 2000
d = √2000 = 20√5

Therefore, the length of the pass with the mower is 20√5 yards.