Question

franke wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft × 32 ft what will be the length of his path to the nearest tenth of a foot?

Explanation:

Step1: Apply Pythagorean theorem

The yard is a rectangle with length \(l = 32\) ft and width \(w=20\) ft. The path is the diagonal of the rectangle. According to the Pythagorean theorem \(d=\sqrt{l^{2}+w^{2}}\), where \(d\) is the length of the diagonal.
Substitute \(l = 32\) and \(w = 20\) into the formula: \(d=\sqrt{32^{2}+20^{2}}\).

Step2: Calculate \(l^{2}\) and \(w^{2}\)

\(32^{2}=32\times32 = 1024\), \(20^{2}=20\times20=400\).
Then \(l^{2}+w^{2}=1024 + 400=1424\).

Step3: Calculate the square - root

\(d=\sqrt{1424}\approx37.7\) (rounded to the nearest tenth).

Answer:

\(37.7\) ft