What are the dimensions of the metal?

Question

a rectangular piece of metal is 25 in. longer than it is wide. squares with sides 5 in. long are cut from the 4 corners and the flaps and folded upward to form an open box. If the volume of the box is 750 inches cube, what were the original dimensions of the piece of metal?

Answer 1

Let L and W be the length and width of the rectangle.  The length is 25 inches longer than the width: L = W + 25. The volume of a rectangular box is:

 

V = Length*Width*Height

 

Where H is the height.  Because 5 inch squares are cut from the corners of the rectangle to fold up the box, the dimensions of the box are:

 

Length = L - 10 in. = (W+25) - 10 = W + 15

Width = W - 10 in.

Height = 5 in.

 

Volume = 750 = (W+15)*(W-10)*5

750 = 5(W² + 5W - 150)

150 = W² + 5W - 150

0 = W² + 5W - 300

 

Factors to:

 

0 = (W+20)(W-15)

W = -20 and 15

 

Since we can't have a negative length, W = 15 inches

 

L = W+ 25  = 15+25 = 40 inches

 

Check:

750 = (40-10)(15-10)(5)

750 = 30*5*5

750 = 750

Check!