SOLUTION: Thomas is going to make an open -top box by cutting squares from four coners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be

Algebra ->  Square-cubic-other-roots -> SOLUTION: Thomas is going to make an open -top box by cutting squares from four coners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be       Log On


   



Question 123332: Thomas is going to make an open -top box by cutting squares from four coners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 ibches, then what size square should be cut from each corner?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
He starts with an area of 11%2A14+=+154in2
The area of the bottom is to be 80 in2
The area of the sides and the removed corners is 154+-+80+=+74
If I call the side of the removed square x,
then the four sides plus the four removed squares is
4x%5E2+%2B+2%2A%2811+-+2x%29+%2B+2%2A%2814+-+2x%29+=+74
4x%5E2+%2B+22+-+4x+%2B+28+-+4x+=+74
4x%5E2+-+8x+%2B+50+=+74
4x%5E2+-+8x+-+24+=+0
x%5E2+-+2x+-+6+=+0
solve by completing the square
x%5E2+-+2x+%2B+1+=+7
%28x+-+1%29%5E2+=+7
x+=+1+%2B+sqrt%287%29in answer
or, using calculator,
x+=+3.646 in