Chapter 9.5, Problem 6STP

For Exercises 1-6, choose the correct letter.

A box shaped like a rectangular prism has a height of 17 in. and a volume of 2720 $i{n}^3.$

The length is 4 inches greater than twice the width. What is the width of the box?

F. $-10$ in.

H. 20 in.

G. $0$ in.

I. 40 in.

To determine

To choose : what is the width of the box

Answer to Problem 6STP

The correct answer is G. $8\text{ in}\text{.}$

Explanation of Solution

Given information :

A box shaped like a rectangular prism has a height of $17\text{ in}.$ and a volume of $2720\text{ in}{.}^3$ . The length is 4 inches greater than twice the width.

Let $w$ be the width of the rectangular prism.

Height of the rectangular prism $=17\text{ in}.$

The length of the rectangular prism $=4+2w$

The volume of the rectangular prism $=2720\text{ in}{.}^3$

  $\begin{array}{l}2720=\left(4+2w\right)w\cdot 17\\ 2720=(4w+2w^2)\cdot 17\\ 2720=68w+34w^2\\ -2720+68w+34w^2=0\\ 34\left(w^2+2w-80\right)=0\\ w^2+2w-80=0\\ w^2+10w-8w-80=0\\ w\left(w+10\right)-8\left(w+10\right)=0\\ \left(w+10\right)\left(w-8\right)=0\end{array}$

  Either       or

  $\begin{array}{l}\left(w+10\right)=0\\ w=-10\text{ in}\end{array}$  $\begin{array}{l}\left(w-8\right)=0\\ w=8\text{ in}\end{array}$

Therefore, the value of width is $8\text{ in}$ because breadth cannot be negative value.

Hence, the correct answer is G. $8\text{ in}\text{.}$ .