Question

(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 square - area formula

For a square, the area formula is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 64$ ft².
\[s^{2}=64\]

Step2: Solve for the side - length

Take the square root of both sides. Since $s>0$ (side - length cannot be negative), we have $s=\sqrt{64}=8$ ft.

Step3: Recall square - perimeter formula

For a square, the perimeter formula 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.
\[4s=12\]

Step4: Solve for the side - length

Divide both sides of the equation $4s = 12$ by 4. We get $s=\frac{12}{4}=3$ ft.

Answer:

(a) 8 ft
(b) 3 ft