Question

A box has a volume of 308 cm cubed. Its height is 4 cm greater than its length. Its length is 3 cm greater than its width. What is the width of the box? SHOW YOUR WORK.

Answer 1

4 cm.

Explanation:

Given:

A box has a volume of 308 cm cubed.

Its height is 4 cm greater than its length.

Its length is 3 cm greater than its width.

Question asked:

What is the width of the box?

Solution:

Let width =
`x\ cm`

Length =
`x+3\ cm`

Height =
`x+3+4=x+7\ cm`

As we know:

`Volume\ of\ box=length* width* height`

`308=(x+3)* x*(x+7)\\ \\ 308=(x^(2) +3x)(x+7)\\ \\ 308=x^(2) (x+7)+ 3x(x+7)\\ \\ 308=x^(3) +7x^(2) +3x^(2) +21x\\ \\ 308=x^(3) +10x^(2) +21x\\ \\ Subtract\ 308\ from\ both\ sides\\ \\ x^(3) +10x^(2) +21x-308=0\\ \\ factor\ left\ side\ of\ equation\\ \\ (x-4)(x^(2) +14x+77)=0\\ \\ Set\ factors\ equal\ to\ 0.\\ \\ x-4=0 \ or\ x^(2) +14x+77=0\\ \\ \\`

As width can never be in negative,
`x= 4\ cm`

By substituting the value:-

Width =
`x\ cm` = 4 cm

Thus, width of the box is 4 cm.