# 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?

Jul 17, 2016

The diagonal would be $20 \sqrt{5} y \mathrm{ds}$ or $44.72 y \mathrm{ds}$

#### Explanation:

Image from SMARTNotebook by @smarterteacher

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.

${a}^{2} + {b}^{2} = {c}^{2}$

${20}^{2} + {40}^{2} = {d}^{2}$

$400 + 1600 = {d}^{2}$

$2000 = {d}^{2}$

$\sqrt{2000} = d$

$\sqrt{10 \cdot 10 \cdot 2 \cdot 2 \cdot 5} = d$

$10 \cdot 2 \sqrt{5} = d$

$20 \sqrt{5} = d$