Chapter 8.6, Problem 3STP

For Exercises $1-5,$ choose the correct letter.

The area of a rectangular swimming pool is $10x^2-19x-15.$

The length of the pool is $5x+3.$

What is the width of the pool?

A. $2x-18$

B. $2x-5$

C. $5x-5$

D. $5x-22$

To determine

To choose : the correct expression for the width of the pool.

A. x- 18   B. 2x- 5   C. 5x- 5   D. 5x- 22

Answer to Problem 3STP

B. 2x- 5

Explanation of Solution

Given information: The area of a rectangular swimming pool is $10x^2-19x-15$ . The length of the pool is 5x+ 3.

Calculation:

Area of rectangular swimming pool can be factorized as follows.

  $\begin{array}{l}10x^2-19x-15\\ =10x^2-25x+6x-15\\ =\left(10x^2-25x\right)+\left(6x-15\right)\\ =5x\left(2x-5\right)+3\left(x-5\right)\\ =\left(5x+3\right)\left(2x-5\right)\end{array}$

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

So, width of rectangular swimming pool is ratio of area of pool to its length.

Width= $=\frac{10x^2-19x-15}{5x+3}=\frac{\left(5x+3\right)\left(2x-5\right)}{5x+3}=2x-5$

Thus, width of the pool is $2x-5$ .