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.

The multiple choice answers won't copy.
Can you help?

Pythagorean Theorem

20^2 + 40^2 = h^2

400 + 1600 = h^2

2000 = h^2

44.72 = h

Thanks much

To solve this problem, we first need to determine the length of the diagonal of the pasture.

The diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.

In this case, the other two sides of the rectangle are the length (40 yards) and the width (20 yards). We can label these sides as "a" and "b."

Using the Pythagorean theorem, we have:

a² + b² = c²

Substituting the values, we have:

20² + 40² = c²

Now, let's calculate:

400 + 1600 = c²

2000 = c²

To find the value of c, we can take the square root of both sides:

√2000 = √c²

√2000 ≈ 44.7 yards ≈ c

Therefore, the length of the diagonal (the pass with the mower) is approximately 44.7 yards.