Question

sandra bought 120 square feet of carpet for a room in her new house. if the room is square, what is the length of each side of the room? recall that the area of a square is calculated by (l^{2}), where (l) is the length of one side. 2√10 feet 2√15 feet 2√20 feet 2√30 feet

Explanation:

Step1: Set up area formula

Let the side - length of the square be $l$. The area formula for a square is $A = l^{2}$, and we know $A = 120$. So, $l^{2}=120$.

Step2: Solve for $l$

Take the square - root of both sides: $l=\sqrt{120}$.

Step3: Simplify the square - root

We can rewrite $120$ as $4\times30$. Then $\sqrt{120}=\sqrt{4\times30}$. Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 4$, $b = 30$), we get $\sqrt{4}\cdot\sqrt{30}=2\sqrt{30}$.

Answer:

D. $2\sqrt{30}$ feet