SOLUTION: 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 folding up the sides. If the area of the bas

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Question 326344: 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 folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
let him cut squares of length x in.
rectangle
length =14
width =11
..
the length after cutting the squares will be 14-2x
the breadth will be 11-2x
(14-2x)(11-2x)=80
154-28x-22x+4x^2 =80
4x^2-50x+154-80=0
4x^2-50x+74=0 ( divide by 2)
2x^2-25x+37=0
we have to find the roots of the equation x1,x2
x1= %2825%2Bsqrt%2825%5E2-296%29%29%2F4
=10.87 in
x2=%2825-sqrt%2825%5E2-296%29%29%2F4
x2=1.71
CHECK
(14-2*1.71)(11-2*1.71)= 80.1 sq.in
so 1.71 side square has to be cut.
x1 is not valid