Chapter 14.8, Problem 19PPS

To determine

To calculate: The perimeter of a square whose area is $x^2+6x+9$square inches.

Answer to Problem 19PPS

The perimeter of the square is $4x+12$

Explanation of Solution

Given Information:

The area of the square is $x^2+6x+9$square inches.

Formula Used:

Perimeter of square $=4\left(\text{side}\right)$

Calculation:

The given area of the square is $x^2+6x+9$square inches.

Find the factors of the expression $x^2+6x+9$

Split $6x$ into two parts such that their product is equal to the product of $x^2$ and $9$.

  $\begin{array}{c}{x}^2+6x+9=x^2+3x+3x+9\\ =x\left(x+3\right)+3\left(x+3\right)\\ =\left(x+3\right)\left(x+3\right)\\ ={\left(x+3\right)}^2\end{array}$

The factors of the trinomial is $x^2+6x+9$are $x+3$. Thus, the length of the sides of the square is $x+3$ inches.

Now, to find the perimeter, use the formula.

  $\begin{array}{c}\text{Perimeter}=4\left(\text{side}\right)\\ =4\times \left(x+3\right)\\ =4x+12\end{array}$

Hence, the perimeter of the square is $4x+12$ inches.