Question

answer the questions below. write your answers in simplest form. (a) a square has an area of 64 ft². what is the length of each side? (b) a square has a perimeter of 4 yd. what is the length of each side?

Explanation:

Step1: Recall area formula for square

The area formula for a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length.
Given $A = 64$ ft², we solve for $s$: $s=\sqrt{A}$.
So, $s=\sqrt{64}$ ft.

Step2: Calculate the side - length

$\sqrt{64}=8$ ft.

Step3: Recall perimeter formula for square

The perimeter formula for a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length.
Given $P = 4$ yd, first convert yards to feet. Since 1 yd = 3 ft, then $P=4\times3 = 12$ ft.
We know $P = 4s$, so $s=\frac{P}{4}$.

Step4: Calculate the side - length

Substitute $P = 12$ ft into $s=\frac{P}{4}$, we get $s=\frac{12}{4}=3$ ft. In yards, since 1 yd = 3 ft, the side - length is 1 yd.

Answer:

(a) 8 ft
(b) 1 yd