Question

The volume of a box is 30 cubic inches. The width of the box is 2 inches less than the length. The height is 3 inches less than the length. Find the length of the box

Answer 1

5 inches

Explanation:

Let the length of the box = l

Width of the box = 2 inches less than the length

= l - 2

Height of the box = 3 inches less than the length

= l - 3

Volume of the box is given by length * width * height

=
`\[l * (l-2) * (l-3)\]`

=
`\[l * (l^(2)-5l+6)\]`

=
`\[l^(3)-5l^(2)+6l)\]`

= 30 cubic inches

Factorizing 30 yields 30 = 2*3*5

This is of the form l * (l-2) * (l-3) where l = 5

So the length of the box is 5 , width is 3 and height is 2 inches respectively.