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.

Answer 1

To find the length of the diagonal pass, we need to use the Pythagorean theorem.

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

Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 20^2 + 40^2
c^2 = 400 + 1600
c^2 = 2000

Taking the square root of both sides:
c = √2000
c = √(400 * 5)
c = 20√5

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