Question

you can calculate the area of a rectangle by multiplying its length by its width. you may recall from previous math classes that a square is one type of a rectangle. the formula for the area of a square is (a = x^{2}), where the value of (x) is the length of one side of the square. you have a square garden with an area of (16x^{2}) square feet. you are trying to determine an expression for the perimeter of the garden. your cousin says: you cant determine the perimeter because there are lots of possible dimensions. your friend says: no, there is only one option. i know what the dimensions are. who is right? explain your thinking. if you can determine the perimeter, include it in your response.

Explanation:

Step1: Find side - length of square

Given area $A = 16x^{2}$ of square, and formula $A=s^{2}$ (where $s$ is side - length). Then $s^{2}=16x^{2}$, so $s = 4x$ (we take the positive value since side - length cannot be negative).

Step2: Calculate perimeter of square

The formula for the perimeter $P$ of a square is $P = 4s$. Substitute $s = 4x$ into the formula, we get $P=4\times4x=16x$.

Answer:

Your friend is right. The perimeter of the square garden is $16x$.