A gardener is mowing a 20 by 40 yard rectangular pasture using a rectangular 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.

a- 10 sq root 20
b- 20 sq root 2
c- 400 sq root 5
d- 20 sq root 5

my answer is D

me too.

To find the length of the mowing pass with the mower, we need to find the length of the diagonal of the rectangular pasture.

Using the Pythagorean theorem, we can find the length of the diagonal.

In a rectangle, the length of the diagonal (D) can be found using the formula:
D = √(length² + width²)

In this case, the length of the pasture is 40 yards and the width is 20 yards. Plugging the values into the formula:

D = √(40² + 20²)
D = √(1600 + 400)
D = √2000

Simplifying the square root of 2000, we can find the answer:

D = √(1000 * 2)
D = √1000 * √2
D = 10√10 * √2
D = 10√20

Therefore, the length of the mowing pass with the mower is 10√20.

So the correct answer is option a - 10√20.