SOLUTION: A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an op

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Question 60963This question is from textbook Algebra for College Students
: A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard. This question is from textbook Algebra for College Students

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the width of the original piece of cardboard. Then its length is x+2
If you were to cut out 2-unit squares from each corner and then fold up the flaps to create an open box, the width of the open box would be (x-4) and its length would be ((x+2)-4), and its height would, of course, be 2.
Now you can write the equation for the volume of the box as:
V+=+%28x-4%29%28%28x%2B2%29-4%29%282%29 But the volume is given as 70 cubic units, so:
%28x-4%29%28%28x%2B2%29-4%29%282%29+=+70 Simplify and solve for x.
%28x-4%29%28x-2%29%282%29+=+70
%28x%5E2-6x%2B8%29%282%29+=+70 Divide both sides by 2.
x%5E2-6x%2B8+=+35 Subtract 35 from both sides.
x%5E2-6x-27+=+0 Solve this quadratic equation for x by factoring.
%28x%2B3%29%28x-9%29+=+0 Applying the zero product principle, you get:
x = -3 Discard this solution as the width can't be a negative value.
x = 9 This is the width of the original piece of cardboard.
x+2 = 11 This is the length of the original piece of cardboard.
Check:
V = (9-4)(11-4)(2) = (5)(7)(2) = 70