SOLUTION: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base

Question 175009: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
2. Thomas is going to make an open-top box by cutting equal squares
from the 4 corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides.
If the area of the base is to be 80 square inches,
then what size square should be cut from each corner?"
Let x = side of the cut-out squares.
The length of the base is: 14 - 2x inches.
The width of the base is: 11 - 2x inches.
The area of the base is 80 in�.
There is our equation: (14 - 2x)(11 - 2x) = 80
and we have the quadratic: 2x� - 25x + 37 = 0
:
in.
:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=329 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10.7845892868043, 1.71541071319574. Here's your graph:

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