SOLUTION: A piece of tin is in the form of a rectangle whose area is 216 square inches. A square of side 2 inches cut from each corner, and an open box is made by turning up the ends and sid

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Question 1097279: A piece of tin is in the form of a rectangle whose area is 216 square inches. A square of side 2 inches cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 224 cubic inches, what is the length of the piece of tin?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2, side length of each square removed from corners
w, width of uncut tin
L, length of uncut tin

system%282%28w-2%2A2%29%28L-2%2A2%29=224%2CwL=216%29


%28w-4%29%28L-4%29=112
wL-4L-4w%2B16=112
-4L-4w%2B16-112%2BwL=0
-4%28L%2Bw%29%2B16-112%2B216=0, substituted for 216=wL;
-4%28L%2Bw%29%2B120=0
L%2Bw-30=0
Substitute for L;
216%2Fw%2Bw-30=0
%28216%2Bw%5E2-30w%29%2Fw=0
%28w%5E2-30w%2B216%29%2Fw=0
The numerator must be 0.
highlight_green%28%28w-12%29%28w-18%29=0%29

Tin's original dimensions are 12 and 18 inch each.