SOLUTION: A square is cut out of each corner of a rectangle sheet of aluminum that is 30 cm by 90 cm. The sides are folded up to form a rectangular container with no top. The area of the bot

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Question 857955: A square is cut out of each corner of a rectangle sheet of aluminum that is 30 cm by 90 cm. The sides are folded up to form a rectangular container with no top. The area of the bottom of the container is 1600cm^2. What are the dimensions of each cut out square? Find the volume of the container? (V= lwh)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x = side length of the square corner piece cut at each of the original rectangle sheet.

Area of the bottom piece becomes highlight_green%28%2830-2x%29%2890-2x%29=1600%29
4%2A4%2815-x%29%2845-x%29=4%2A4%2A100
%2815-x%29%2845-x%29=100
675-60x%2Bx%5E2=100
x%5E2-60x%2B575=0
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discriminant, 3600-4*575=572=2*2*143
x=%2860%2Bsqrt%282%2A2%2A143%29%29%2F2
x=%2860%2B2%2Asqrt%28143%29%29%2F2
highlight%28x=30%2Bsqrt%28143%29%29

Volume: expect this to be highlight%28highlight%28%2830%2Bsqrt%28143%29%29%2A1600%29%29.
That is, the known base area multiplied by the height of x, which we just solved for.