SOLUTION: Open-Top Box: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and foldiing up the ssides. If t
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-> SOLUTION: Open-Top Box: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and foldiing up the ssides. If t
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Question 204283This question is from textbook Elementary & Intermediate Algebra
: Open-Top Box: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and foldiing up the ssides. If the area of the base is to be 80 square inches, then what size square should be cute from each corner This question is from textbook Elementary & Intermediate Algebra
Let represent the measure of the side of one of the cut-out squares. Since each of the dimensions of the original piece of cardboard will be reduced by to form the base of the box, the dimensions of the base of the box will be and . Since the area of a rectangle is length times width and we know the area of the base must be 80 square inches, we can write:
Multiply the binomials and collect like terms:
This does not factor conveniently, so use the quadratic formula:
Both roots are real and positive, but one of them is way too large, namely meaning that the cutout squares would overlap and you would have no box at all. So exclude this root as extraneous having been introduced by the act of squaring the variable. The other root, is the correct answer.
