Question

joey measured the floor of his storage unit, which is rectangular. it is 9.4 meters wide and 9.8 meters from one corner to the opposite corner. how long is the storage unit? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Apply Pythagorean theorem

Let the length be \(l\), width \(w = 9.4\) meters and diagonal \(d=9.8\) meters. By Pythagorean theorem \(l^{2}+w^{2}=d^{2}\), so \(l^{2}=d^{2}-w^{2}\).

Step2: Substitute values

Substitute \(d = 9.8\) and \(w = 9.4\) into the formula: \(l^{2}=(9.8)^{2}-(9.4)^{2}\).
First, calculate \((9.8)^{2}=96.04\) and \((9.4)^{2}=88.36\). Then \(l^{2}=96.04 - 88.36=7.68\).

Step3: Solve for \(l\)

Take the square root of \(l^{2}\), \(l=\sqrt{7.68}\approx2.8\)

Answer:

\(2.8\)