SOLUTION: I have a piece of cardboard, twice as long as it is wide. I will cut 4x4 suqares out of each corners, so I fold up the corners and use it as a tray. The volume of the tray will be

Question 633011: I have a piece of cardboard, twice as long as it is wide. I will cut 4x4 suqares out of each corners, so I fold up the corners and use it as a tray. The volume of the tray will be 96 cubic inches. How large is the piece of cardboard?
Answer by graphmatics(170) (Show Source): You can put this solution on YOUR website!
Let x be the width of the cardboard. 2x is the length of the card. After cutting out the 4 by 4s on the corners and creating the tray the area of the bottom of the tray will be (x-8)(2x-8). The height of the tray is 4. The volume of the tray is (x-8)(2x-8)4. Because the volume of the tray is 96 we have that (x-8)(2x-8)(4)=96 so . . . . We solve this quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10, 2. Here's your graph:

. We must select x=10 because x must be greater than 8. The cardboard dimensions are 10 and 20.
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