Question 123789: Hi, I have hard time picturing the word problem in my head. Could you please help me solving it?
Marcos wants to make an open box by cutting equal squares from each corner of a rectangular piece of cardboard measuring 12 by 20 inches. If the box needs a base of 84 sq. inches, what size square should be cut from each corner?
Thank you very much!
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! This one was hard for me to picture in my head, too, so I drew a picture on paper. I suggest you do the same, or the following will make little to no sense. I drew a rectangle and then labeled one side 20 and the other 12. Then I drew a square in each corner, and labeled each edge not on the rectangle's edge x. So each square has 2 x's. Now those are the squares that will be cut off, and the small rectangles sticking out to the side will be folded up to make the sides of the box. So I drew in the base of that box by continuing the lines that are there from the squares. Now I looked at that centered rectangle. The area of that should be 84. The length is 20-2x and the width is 12-2x. So (20-2x)(12-2x)=84.
240-64x+4x^2=84
Divide by 4: 40-16x+x^2=21
x^2-16x+39=0
Factor: (x-3)(x-13)=0
x can't be 13 because the width of the big rectangle is only 12, and we are cutting off x from each end. So x=3. So you need to cut off a 3x3 square at each corner.
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