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 336 in​, what were the original dimensions of the piece of​ metal?

Answer 1

The dimensions of the piece of metal can be represented by:

x and x + 5

Now, 1 in squares are being cut out of each corner.

So the new dimensions are:

L = x - 2

1 in from each side

and

W = x + 5 - 2

1 in from each side

W = x + 3

When you fold it up, the height becomes 1.

H = 1

Now plug this into the volume formula.

V = L • W • H

336 = ( x - 2 ) • ( x + 3 ) • 1

336 = x² - 2 x + 3 x - 6

x² + x - 6 = 336

Subtract 336 to both sides.

x² + x - 342 = 0

The solutions are:

x = - 19

and

x = 18

The length cannot be negative, so you have to reject the solution x = - 19.

x = 18m

Your original dimension for the piece of metal are:

18m by 18 + 5m

18m by 23m