Question

1. a rectangular rug is 12 feet long and has a diagonal measure of 15 feet. determine the area, in square feet, that the rug covers. enter your response in the gridded area.

Explanation:

Step1: Use Pythagorean theorem to find width

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Let the length \(a = 12\) (feet), the diagonal \(c=15\) (feet), and the width be \(b\). Then \(b^{2}=c^{2}-a^{2}\). Substitute the values: \(b^{2}=15^{2}-12^{2}\). Calculate \(15^{2}=225\) and \(12^{2}=144\). So \(b^{2}=225 - 144=81\). Then \(b=\sqrt{81}=9\) (feet).

Step2: Calculate the area of the rectangle

The area formula of a rectangle is \(A=\text{length}\times\text{width}\). Substitute length \(l = 12\) (feet) and width \(w = 9\) (feet). So \(A=12\times9 = 108\) (square - feet).

Answer:

\(108\)