Question

A rectangular piece of metal is 15 in longer than it is wide. Squares with sides

3 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1350 in3​, what were the original dimensions of the piece of​ metal?

Answer 1

Let the width be
`w` inches and the length be
`w+15` inches.

So, the dimensions of the box are
`w-6`,
`w+9`, and
`3` inches.

`3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21`

Rejecting the negative case,
`w=21`.

So, the dimensions are 21 by 36 inches.