Solving volume with quadratic formulas

Question

the length of the rectangular piece of sheet metal is 3 in longer its width a square piece that measures 1 in on each side is cut from each corner then the sides are turned up to make a box with volume 70 on find the length and width of the original piece of metal

Answer 1

 Length is L=w+3

 

 

 Post fabrication:

   Length is w+3-1-1 = w+1

 

  Width is w-2

 

 Height is 1

 

The volume of the box is (w+1)(w-2)*1 = 70

                                     w^2 - 2w + w - 2 = 70

                                     w^2 - w - 72 = 0

                                      (  w      -    9)( w   +     8  ) = 0

 

w+8 = 0 results in negative measures

w-9=0 ---> w=9

 

ORIGINAL DIMENSIONS

Width is 9.

Length is 12.

 

Post fabrication:

 Width is 7, Length is 10, Height is 1 ---> volume is 70