SOLUTION: Thomas is going to make an open - box by cutting equal squares from th four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the base is to be 80 sq

Question 166435: Thomas is going to make an open - box by cutting equal squares from th four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the base is to be 80 square inches, then what size should be cut from each corner?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Thomas is going to make an open - box by cutting equal squares from th four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the base is to be 80 square inches, then what size should be cut from each corner?
11x14
base w/corners cut:
(11-2x) by (14-2x)
.
if the base is to be 80 sq inches:
80 = (11-2x)(14-2x)
80 = 154 - 22x -28x + 4x^2
80 = 154 - 50x + 4x^2
80 = 4x^2- 50x + 154
0 = 4x^2- 50x + 74
0 = 2x^2- 25x + 37
Solving using the quadratic equation yields:
x = {10.7845892868043, 1.71541071319574}
.
solution:
10.78 inches
or
1.72 inches
.
Details of 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=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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