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

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) (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:
But the volume is given as 70 cubic units, so:
Simplify and solve for x.

Divide both sides by 2.
Subtract 35 from both sides.
Solve this quadratic equation for x by factoring.
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

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