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?

1 Answer
Jul 17, 2016

Answer:

The diagonal would be #20sqrt5 yds# or #44.72 yds#

Explanation:

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To determine the length of the gardeners path across the diagonal of the rectangular field we must look at the right triangle created by the length and width of the rectangle and the diagonal cut by the gardener.

We can then use the Pythagorean Theorem to solve for the missing value.

#a^2 + b^2 = c^2#

#20^2 + 40^2 = d^2#

#400 + 1600 = d^2#

#2000 = d^2#

#sqrt(2000) = d#

#sqrt(10*10*2*2*5) = d#

#10*2sqrt5=d#

#20sqrt5=d#