A gardener is mowing a 20 yard-by-40 yd 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.

Please explain to me how to solve. Thanks.

Use the Pythagorean Theorem.

a^2 + b^2 = c^2

20^2 + 40^2 = c^2

400 + 1600 = c^2

2000 = c^2

44.7 = c

To find the length of the path, we need to determine the length of the diagonal of the rectangular pasture.

We can use the Pythagorean theorem to find the length of the diagonal triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the two sides are the width (20 yards) and length (40 yards). Let's label the diagonal as 'd'.

Using the formula of the Pythagorean theorem:
d^2 = 20^2 + 40^2

Simplifying this equation:
d^2 = 400 + 1600
d^2 = 2000

To get the value of 'd', we take the square root of both sides of the equation:
d = √2000

Now, we simplify the square root of 2000. Pairing the prime factors, we have:
d = √(2 * 2 * 2 * 5 * 5 * 2 * 5)
d = 2 * 5 * √(2 * 5)
d = 10 * √(10)

Therefore, the length of the mowing path is 10√10 yards, which is the simplified form.