Question

16 multiple choice 2 points
find the length of a rectangle whose width is 7 inches and whose diagonal is 16 inches. (round your answer to the nearest tenth of an inch.)

Explanation:

Step1: Apply Pythagorean theorem

Let the length be \(l\), width \(w = 7\) inches and diagonal \(d=16\) inches. By Pythagorean theorem \(l^{2}+w^{2}=d^{2}\), so \(l^{2}=d^{2}-w^{2}\).
Substitute \(d = 16\) and \(w = 7\): \(l^{2}=16^{2}-7^{2}\).
Calculate \(16^{2}=256\) and \(7^{2} = 49\). Then \(l^{2}=256 - 49=207\).

Step2: Solve for \(l\)

Take square root of both sides: \(l=\sqrt{207}\).
Using a calculator, \(\sqrt{207}\approx14.4\)

Answer:

\(14.4\) inches