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?
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