A gardener is mowing a 20-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.

Answer 1

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

In this case, the two sides of the pasture are 20 yards and 40 yards. Let's assume the length of the diagonal is x yards.

So, using the Pythagorean theorem, we have:
x^2 = 20^2 + 40^2
x^2 = 400 + 1600
x^2 = 2000

Taking the square root of both sides to find the length of the diagonal:
x = sqrt(2000) = sqrt(400 * 5) = sqrt(400) * sqrt(5) = 20 * sqrt(5)

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