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.

Question

A.10 sq rt 20
B.20 sq rt 2
C.400 sq rt 5
D.20 sq rt 5

Answer 1

To find the length of this diagonal pass with the mower, we can use the Pythagorean Theorem.

Let the length of the pasture be 20 yards and the width be 40 yards. The diagonal pass with the mower will be the hypotenuse of a right triangle where the length and width are the two legs.

Using the Pythagorean Theorem:
diagonal length^2 = length^2 + width^2
diagonal length^2 = 20^2 + 40^2
diagonal length^2 = 400 + 1600
diagonal length^2 = 2000

Taking the square root of both sides:
diagonal length = sqrt(2000)

Simplifying sqrt(2000):
sqrt(2000) = sqrt(1000 * 2)
sqrt(2000) = sqrt(1000) * sqrt(2)
sqrt(2000) = 10 sqrt(100) * sqrt(2)
sqrt(2000) = 10 * 10 * sqrt(2)
sqrt(2000) = 100 sqrt(2)

Therefore, the length of the diagonal pass with the mower is 100 sqrt(2) yards, which is equivalent to 20 sqrt(5) yards.

So the correct answer is:
D. 20 sqrt(5)