Question

challenge yael used to have a square garage with 232 ft² of floor space. she recently built an addition to it. the garage is still a square, but now it has 50% more floor space. what was the length of one side of the garage originally? what is the length of one side of the garage now? what was the percent increase in the length of one side? one side of the garage was originally ft long. (round to the nearest tenth as needed.)

Explanation:

Step1: Find original side - length

Since the original garage is square with area $A = 232$ square - feet, and the area formula for a square is $A = s^{2}$ (where $s$ is the side - length), then $s=\sqrt{A}$. So, $s=\sqrt{232}\approx15.2$ feet.

Step2: Find new area

The new garage has 50% more floor space. The new area $A_{new}=(1 + 0.5)\times232=1.5\times232 = 348$ square - feet.

Step3: Find new side - length

Since the new garage is also square, and $A_{new}=s_{new}^{2}$, then $s_{new}=\sqrt{A_{new}}=\sqrt{348}\approx18.6$ feet.

Step4: Calculate percent increase

The percent increase formula is $\text{Percent Increase}=\frac{s_{new}-s}{s}\times100\%$. Substitute $s_{new}\approx18.6$ and $s\approx15.2$ into the formula: $\text{Percent Increase}=\frac{18.6 - 15.2}{15.2}\times100\%=\frac{3.4}{15.2}\times100\%\approx22.4\%$.

Answer:

The length of one side of the original garage was approximately $15.2$ feet. The percent increase in the length of one side is approximately $22.4\%$.