Question

the area of a square is 108 ft2. which of the following represents the length of one side? a. 27 feet b. 54 feet c. 6√3 feet d. 36√3 feet

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length.

Step2: Solve for side - length

Given $A = 108$, then $s=\sqrt{A}=\sqrt{108}$.

Step3: Simplify the square - root

We can rewrite $108$ as $36\times3$. So, $\sqrt{108}=\sqrt{36\times3}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 36$, $b = 3$), we get $\sqrt{36}\times\sqrt{3}=6\sqrt{3}$.

Answer:

C. $6\sqrt{3}$ feet