Question

The perimeter of a square is represented by the expression 4x +24. What is the length of one sideof the square?

Answer 1

Concept:

The formula for the perimeter of a square with side L is given below as

`P_{\text{square}}=4* L`

From the question, the perimeter of the square is given below as

`P_{\text{square}}=4x+24`

Step 1: Substitute the expression above in the formula of the perimeter

`\begin{gathered} P_{\text{square}}=4* L \\ P_{\text{square}}=4x+24 \\ \text{Therefore,we will have} \\ 4* L=4x+24 \\ 4L=4x+24 \end{gathered}`

Step 2: Factorize the perimeter 4x+24 by involving brackets

`\begin{gathered} 4L=4x+24 \\ 4L=4((4x)/(4)+(24)/(4)) \\ 4L=4(x+6) \end{gathered}`

Step 3:

To find the value of the length of one side of the square, we will divide both sides by 4

`\begin{gathered} 4L=4(x+6) \\ (4L)/(4)=(4(x+6))/(4) \\ L=x+6 \end{gathered}`

Hence,

The length of one side of the square = x+6