Question

A rectangular piece of metal is 10 in longer than it is wide. Squares will side 2 in long are cut from the four corners and the flaps are fielded upward to form an open box. If the volume of the box is 1008 in^3, what were the original dimensions of the piece of mental

1. The original dimensions of the piece of metal are; 22 inches is the width of the rectangular metal and 32 inches is the length.

### How to Maximize Volume?

Let x = the width of the rectangular piece of metal
then
(x + 10) = the length
Removing the 2 inches squares would make the dimensions of the box:
(x – 4) by (x + 10-4) or (x – 4) by (x + 6)
The height of the box = 2 inches
The volume equation is; V = L * W * h
Thus;
(x + 6) * (x – 4) * 2 = 1008
divide both sides by 2
(x + 6)(x – 4) = 504
FOIL
x² – 4x + 6x – 24 = 504
x² + 2x – 24 – 504 = 0
x² + 2x – 528 = 0
Using quadratic equation calculator, this will factor to
(x + 24)(x – 22) = 0
We will pick the positive solution;
x = 22 inches is the width of the rectangular metal
then
32 inches = the length