Question

answer the questions below. write your answers in simplest form. (a) a square has a perimeter of 100 yd. what is the length of each side? yd (b) a square has an area of 144 ft². what is the length of each side? ft

Explanation:

Step1: Recall perimeter formula for square

The perimeter $P$ of a square is $P = 4s$, where $s$ is the side - length. Given $P = 100$ yd. We solve for $s$ by the equation $100=4s$.

Step2: Solve for side - length

Dividing both sides of the equation $100 = 4s$ by 4, we get $s=\frac{100}{4}=25$ yd.

Step3: Recall area formula for square

The area $A$ of a square is $A=s^{2}$, where $s$ is the side - length. Given $A = 144$ ft². We solve for $s$ by the equation $s^{2}=144$.

Step4: Solve for side - length

Taking the square root of both sides of the equation $s^{2}=144$, since $s>0$ (side - length cannot be negative), we have $s = \sqrt{144}=12$ ft.

Answer:

(a) 25 yd
(b) 12 ft