Chapter 10.2, Problem 5STP

For Exercises 1-5, choose the correct letter.

A gardener is mowing a 20 yd-by-40 yd rectangular pasture using a diagonal pattern. He mows from one comer of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form.

A. $10\sqrt{20}$

B. $20\sqrt{2}$

C. $400\sqrt{5}$

D. $20\sqrt{5}$

To determine

To choose the correct answer.

Answer to Problem 5STP

D) $20\sqrt{5}$

Explanation of Solution

Given information:

A gardener is mowing a $20$ yard 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.”

A) $10\sqrt{20}$

B) $20\sqrt{2}$

C) $400\sqrt{5}$

D) $20\sqrt{5}$

The diagonal is:

$\begin{array}{l}d=\sqrt{{20}^2+{40}^2}\\ d=\sqrt{400+1600}\\ d=\sqrt{2000}\\ d=\sqrt{4\times 4\times 5\times 5\times 5}\\ d=20\sqrt{5}\end{array}$

Hence, the correct answer is $20\sqrt{5}$ .