Question

1. 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 = s^{2} ), where the value of ( s ) 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. view image description two students are conversing in front of lockers with two thought bubbles. - one thought bubble states: your cousin says: \you cant remember the perimeter because there are lots of possible dimensions.\ - the second thought bubble states: your friend says:

o, 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 the side length of the square

Since the area of a square is \(A = s^{2}\) and \(A=16x^{2}\), then \(s^{2}=16x^{2}\). Taking the square root of both sides, \(s = 4x\) (we consider the non - negative root because length cannot be negative).

Step2: Calculate the perimeter of the square

The perimeter of a square is \(P = 4s\). Substituting \(s = 4x\) into the formula, we get \(P=4\times4x=16x\).

Answer:

Your friend is right. The side length of the square garden \(s=\sqrt{16x^{2}} = 4x\) (since length \(s>0\)). The perimeter of a square \(P = 4s\), so \(P=4\times4x=16x\). There is only one possible set of dimensions for a square with area \(16x^{2}\) (side length \(4x\)), so the perimeter is \(16x\) feet.