SOLUTION: from a rectangular sheet of metal 16 inches long and 8 inches wide an open rectangular box is made by cutting squares of equal area from the four corners and folding up the ends. I

Question 1029051: from a rectangular sheet of metal 16 inches long and 8 inches wide an open rectangular box is made by cutting squares of equal area from the four corners and folding up the ends. If the area of the base of the box is 50 square inches, find the total area of the discarded squares, round your answer to the nearest thousandth.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The cuts will come from each side, and if they are x inches long, the new base will be (16-2x) by (8-2x). The height will be x.
The area of the base is the product of the two terms: 128-48x+4x^2=50
4x^2-48x+78=0
2x^2-24x+39=0
x=(1/4)* (24 +/- sqrt (576-312); sqrt 264=16.241
x=(1/4)(7.759), since adding would not make sense, given the dimensions.
x=1.939
4x^2 is the area of the discarded squares, or 15.023 sq inches (round at end)
The dimensions of the base are approximately 12.122 by 4.122 and that is an area of 49.97 sq in.

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