Question

A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 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 500 in3​, what were the original dimensions of the piece of​ metal?

Answer 1

Answer: 22 in by 27 in

Explanation:

Let the dimensions of the rectangle be
`x` by
`x+5`.

It follows that the dimensions of the box are
`x-2`,
`x+3`, and
`1`.

`\implies (x-2)(x+3)=500\\\\x^2+x-6=500\\\\x^2+x-506=0\\\\(x+23)(x-22)=0\\\\x=-23, 22\\\\x > 0 \implies x=22`

So, the original dimensions were 22 in by 27 in.