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

Question 176011This question is from textbook
: thomas is going to make an open top box by cutting equal squares from the four corners on an 11 inch by 14 inch sheet of cardboard and folding up the sides. if the area of the base is to be 80 sqare inches then what size should be cut from each corner?

This question is from textbook

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
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
The Quadratic Formula gives us: x = �(25 � √239)
The smaller root is the answer: x = �(25 - √329) ≈ 1.7154 inches

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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