The dimensions of the original piece of cardboard are 24 inches by 12 inches
How to determine the dimensions of the original piece of cardboard?
The given parameters are:
Length (l)= Width (w) + 12
Length of the square cut out = 6
Volume of box, V = 1728
The volume of the box is then calculated as
V = Length of squares * Length * Width
This gives
V = 6 * (w + 12) * w
So, we have:
6 * (w + 12) * w = 1728
Divide both sides by 6
(w + 12) * w = 288
Expand
w^2 + 12w - 288 = 0
Using a graphing calculator, we have:
w = 12
Substitute w = 12 in l = w + 12
Evaluate
l = 12 + 12
l = 24
Hence, the dimensions of the original piece of cardboard are 24 inches by 12 inches
Read more about volume at:
https://brainly.com/question/16563257
#SPJ1
Complete question
Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner. The length of the original piece of cardboard is 12 inches more than the width. If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.
