Question

challenge yossi used to have a square garage with 334 ft² of floor space. he 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 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 the original side - length

The area formula for a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given the original area $A_1=334$ square feet. So, we solve for $s_1$:
\[s_1=\sqrt{A_1}=\sqrt{334}\approx18.3\] feet.

Step2: Find the new area

The new area $A_2$ is 50% more than the original area. So, $A_2=(1 + 0.5)A_1$. Since $A_1 = 334$, then $A_2=1.5\times334 = 501$ square feet.

Step3: Find the new side - length

Using the area formula for a square again, we solve for $s_2$ when $A_2 = 501$. So, $s_2=\sqrt{A_2}=\sqrt{501}\approx22.4$ feet.

Step4: Calculate the percent increase in side - length

The percent increase formula is $\text{Percent Increase}=\frac{s_2 - s_1}{s_1}\times100\%$. Substitute $s_1\approx18.3$ and $s_2\approx22.4$ into the formula:
\[\text{Percent Increase}=\frac{22.4 - 18.3}{18.3}\times100\%=\frac{4.1}{18.3}\times100\%\approx22.4\%\]

Answer:

One side of the garage was originally approximately $18.3$ ft long.
The length of one side of the garage now is approximately $22.4$ ft.
The percent increase in the length of one side is approximately $22.4\%$.