Find the length and width of the original piece of cardboard.

Question

The length of a rectangular piece of cardboard is 3in longer than its width. A square piece that measures 2in on each side is cut from each corner and then the sides are turned up to make an uncovered box with volume 80in^3. find the length and width of the original piece of cardboard.

Answer 1

Let L = the original length of the cardboard and W = its width.

 

L = W + 3    [The length is 3in longer than its width]

 

Now we cut 2 inch squares out of each corner and fold them up into an open box

    _____

__|        |__

|                | 

|                |  box length = L-4 = W+3-4 = W-1

|_           __| 

   |_____|       

 box width 

  = W-4

 

The volume = (box length)*(box width)*(box height=2 inches):

(W-1)(W-4)(2) = 80

W² - 5W + 4 = 40

W² - 5W - 36 = 0

Factors to:

(W-9)(W+4) = 0

W = 9 or -4

W = 9 inches (can't have a negative length)

L = W + 3 = 12 inches