Question

answer the questions below. write your answers in simplest form. (a) a square has an area of 9 cm². what is the length of each side? (b) a square has a perimeter of 32 m. what is the length of each side?

Explanation:

Step1: Recall square - area formula

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

Step2: Solve for side - length in part (a)

Given $A = 9\ cm^{2}$, then $s=\sqrt{A}$. Substituting $A = 9\ cm^{2}$, we get $s=\sqrt{9\ cm^{2}} = 3\ cm$.

Step3: Recall square - perimeter formula

The perimeter formula for a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length.

Step4: Solve for side - length in part (b)

Given $P = 32\ m$, and $P = 4s$. Then $s=\frac{P}{4}$. Substituting $P = 32\ m$, we have $s=\frac{32\ m}{4}=8\ m$.

Answer:

(a) 3 cm
(b) 8 m