Chapter 8.5, Problem 6STP

For Exercises $1-7,$ choose the correct letter.

The area of a garden is given by the trinomial $g^2-2g-24$.

The garden’s length is $g+4.$

What is the garden’s width?

F. $g-2$

G. $g-6$

H. $g-8$

I. $g+2$

To determine

To choose : the correct width of the garden.

F.$g-2$   G. $g-6$   H. $g-8$   I. $g+2$

Answer to Problem 6STP

G. $g-6$

Explanation of Solution

Given expression: The area of a garden is given by the trinomial $g^2-2g-24$ .The garden’s length is g+ 4.

Calculation:

Area of the rectangular garden can be factorized as follow.

  $\begin{array}{l}A=g^2-2g-24\\ A=g^2-6g+4g-24\\ A=\left(g^2-6g\right)+\left(4g-24\right)\\ A=g\left(g-6\right)+4\left(g-6\right)\\ A=\left(g-6\right)\left(g+4\right)\end{array}$

We know that area of rectangle is product of the length of rectangle and width of rectangle.

Therefore, width of the garden is ratio of area of garden to the length of garden and is evaluated as

Width $=\frac{g^2-2g-24}{g+4}=\frac{\left(g-6\right)\left(g+4\right)}{g+4}=g-6$

Thus, width of the garden is $g-6$ .