Question

a stage designer paid $3 per square foot for flooring to be used in a square room. if the designer spent $510 on the flooring, about how long is a side of the room? round to the nearest foot.

Explanation:

Step1: Calculate area of flooring

We know the cost per - square foot and total cost. Let the area of the flooring be $A$. The cost per square foot is $3$ dollars and the total cost is $510$ dollars. Using the formula $Total\ cost=Cost\ per\ square - foot\times Area$, we have $A=\frac{510}{3}$.
$A = 170$ square feet.

Step2: Find side - length of square room

Since the room is square and the area of a square is $A = s^{2}$ (where $s$ is the side - length of the square), then $s=\sqrt{A}$. Substituting $A = 170$ into the formula, we get $s=\sqrt{170}$.
$s\approx13$ feet (rounded to the nearest foot).

Answer:

13 feet