College Algebra

Question

She makes boxes from rectangular sheets of cardboard from which she cuts 6inch squares from each corner. The length of the original piece of cardboard is 12inch more than the width. If the volume of the box is 1728 in cubes, determine the dimensions of the original piece

Answer 1

To better understand this problem, draw a picture and label the dimensions.

 

     xxxxxxxxxxxxx

  xxxxxxxxxxxxxxxxx

  xxxxxxxxxxxxxxxxx      L = W+12   

  xxxxxxxxxxxxxxxxx

    xxxxxxxxxxxxxx

 

             W

 

The volume is length*width*height       [use new values]

 

  V = (new length)*(new wisth)*(new height)

 

   V = (W+12 -6 -6 )*(W -6 -6)*(6)

   V = W*(W-12)*(6)

   V = 6W² - 72W

 

And,

     6W² - 72W = 1728

     W² -12W - 288 = 0

    (W-24)(W+12) = 0                [either factor or use Quadratic Formula]

 

  Either  W=24  or  W=-12  or  buth          [Mul;tiplicative Property of Zero]

 

   The width (W) cannot be negative, so W=24

              That means  L=36            [because L = W+12]

 

Check:

  Is  (36 - 6 - 6)*(24 - 6 - 6)(6)  = 1728    ?

          24*(12)(6) = 1728    ?yes