Chapter 8.6, Problem 36PPS

To determine

To find: An expression for the perimeter of a rectangle with the given area.

Answer to Problem 36PPS

  $2\left(2x+13\right)$

Explanation of Solution

Given:

  $A=x^2+13x-90$

Calculation:

The area of rectangle is given by $x^2+13x-90$

Find the factors of this expression

Rewrite the middle term as $13x=18x-5x$ . So, the polynomial becomes

  $x^2+18x-5x-90$

Make group as shown below

  $\left(x^2+18x\right)+\left(-5x-90\right)$

Factor out the GCF from each of the group

  $x\left(x+18\right)-5\left(x+18\right)$

Finally, factored out the common factor

  $\left(x+18\right)\left(x-5\right)$

Now, the area of rectangle is given by

  $A=lw$

Comparing this with the above factored form of area to find the expression for the length and width of the rectangle

  $\begin{array}{l}l=\left(x+18\right)\\ w=\left(x-5\right)\end{array}$

Therefore, the perimeter of the rectangle is given by the expression

  $\begin{array}{l}2\left(l+w\right)\\ =2\left(x+18+x-5\right)\\ =2\left(2x+13\right)\end{array}$