Chapter 8.6, Problem 4LC

To determine

To simplify: simply the given question using factorization

Answer to Problem 4LC

Dimensions are $\left(2x-9\right)$ and $\left(3x+8\right)$

Explanation of Solution

Given information: we have given

Area of rectangle is $6x^2-11x-72$

Let the sides of rectangle be l and b

As we know

  $\text{Area}\text{of}\text{rectangle}=\text{length×breadth}$

Also area of rectangle= $6x^2-11x-72$

Use factoring

  $\begin{array}{c}6x^2-11x-72=6x^2-27x+16x-72\\ =3x\left(2x-9\right)+8\left(2x-9\right)\\ =\left(2x-9\right)\left(3x+8\right)\end{array}$

Comparing both the equations we get

  $l=\left(3x+8\right)$ and $b=\left(2x-9\right)$

Therefore dimensions are $\left(3x+8\right)$ and $\left(2x-9\right)$