SOLUTION: Hello. I'm having some trouble figuring out the following problem: A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 inch square

Question 196348: Hello.
I'm having some trouble figuring out the following problem:
A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 inch squares from each corner and folding up the sides, as shown in the figure. The box is to hold 144 in3. How big a piece of cardboard is needed?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 inch squares from each corner and folding up the sides, as shown in the figure. The box is to hold 144 in3. How big a piece of cardboard is needed?
.
You must draw a diagram of the problem -- it'll help you see the problem.
.
Let x = length of one side of the square cardboard
then
4 in = height
width = x-8
length = x-8
.
volume = height*width*length
.
144 = 4(x-8)(x-8)
144 = 4(x^2-16x+64)
36 = x^2-16x+64
0 = x^2-16x+28
0 = (x-14)(x-2)
x ={2,14}
We toss out 2 leaving:
x = 14 inches
.
Cardboard is 14x14 inches
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