Question

sam built a walkway out to a firepit in his backyard. he used square stepping stones that are 1 foot on a side. he placed 60 stones in a pattern that is 5 feet wide by 12 feet long.

if sam’s walkway is rectangular, what is the length of the diagonal? record your answer in feet to the nearest whole number.

Explanation:

Step1: Identify the rectangle's sides

The walkway is a rectangle with width \( w = 5 \) feet and length \( l = 12 \) feet.

Step2: Apply the Pythagorean theorem

For a right - triangle (formed by the length, width, and diagonal of the rectangle), the Pythagorean theorem is \( d=\sqrt{l^{2}+w^{2}} \), where \( d \) is the diagonal. Substitute \( l = 12 \) and \( w = 5 \) into the formula:
\( d=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169} \)

Step3: Calculate the square root

\( \sqrt{169}=13 \)

Answer:

13