Question

challenge yael used to have a square garage with 320 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

For a square, area $A = s^{2}$, where $s$ is the side - length. Given original area $A_1=320$ ft². So, $s_1=\sqrt{A_1}=\sqrt{320}\approx17.9$ ft.

Step2: Find new area

The new area $A_2$ is 50% more than the original area. So, $A_2=(1 + 0.5)A_1=1.5\times320 = 480$ ft².

Step3: Find new side - length

Since $A_2=s_2^{2}$, then $s_2=\sqrt{A_2}=\sqrt{480}\approx21.9$ ft.

Step4: Find percent increase in side - length

The percent increase formula is $\text{Percent Increase}=\frac{s_2 - s_1}{s_1}\times100\%$. Substitute $s_1\approx17.9$ ft and $s_2\approx21.9$ ft. $\text{Percent Increase}=\frac{21.9 - 17.9}{17.9}\times100\%=\frac{4}{17.9}\times100\%\approx22.3\%$.

Answer:

One side of the garage was originally approximately $17.9$ ft long.
The length of one side of the garage now is approximately $21.9$ ft.
The percent increase in the length of one side is approximately $22.3\%$.