SOLUTION: An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of

Question 188520: An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of the sides of the squares?
a) Draw and label a picture
b) Find the length of the squares
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I've been trying to help my son who is in 11th grade, but I can't. The closest he came to coming to a solution is:
330-30x-44x+4x(squared)=110in(squared)
(sorry I don't know where the "squared" character is on my keyboard
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An open box is made from a piece of cardboard 15 inches by 22 inches by cutting out squares from each corner. If the resulting bas has area of 110in(squared), what is the length of the sides of the squares?
a) Draw and label a picture
b) Find the length of the squares
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When the squares are cut out, the bottom will be (15-2x)*(22-2x) = 110
4x^2 - 74x + 330 = 110
4x^2 - 74x + 220 = 0
2x^2 - 37x + 110 = 0
x^2 - 18.5x + 55 = 0

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=122.25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 14.778336096874, 3.721663903126. Here's your graph:

The sides of the squares cut out = 3.72166... inches

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