Question

A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be?

Answer 1

Answer:

The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

Step-by-step explanation:

Let the width of rectangular solid be x

We are given that the length of the container must be one meter longer than the width

So, Length of solid = x+1

We are also given that height must be one meter greater than twice the width

So, Height of solid = 2x+1

So, Volume of solid = $Length \times Width \times height$

Volume of solid = $(x+1) \times x \times (2x+1)$

Volume of solid =$(x^2+x)(2x+1)$

Volume of solid =$2x^3+x^2+2x^2+x=2x^3+3x^2+x$

We are given that  a rectangular solid must have a volume of 84 cubic meters

So, $2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0$

On equating

x-3=0

x=3

So, Length of solid = x+1=3+1 = 4 feet

Height of solid = 2x+1 =2(3)+1=7 feet

Width of solid = 3 feet

Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.