SOLUTION: your making a metal tray by cutting equal squares from each corner of a rectangular sheet of metal. what should be the dimension of each cut out square be for the volume of the tra

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Question 820971: your making a metal tray by cutting equal squares from each corner of a rectangular sheet of metal. what should be the dimension of each cut out square be for the volume of the tray to be 60 cubic inches
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You have too many variables as described, but to begin,
Let h = one length of the original rectangle,
Let v = perpendicular length of the original rectangle,
let x = the side of the square to remove from each corner of the original rectangle.
Let c = the expected capacity of the tray when finished, in this case, 60 cubic inches.

Draw a picture of this rectangle and its corner, square cut pieces to be removed.
...
...

One direction along the bottom will be h-2x, and the other direction along the bottom will be v-2x. The up-down direction for the tray will be x. The equation which will describe your expected c is:
%28h-2x%29%28v-2x%29x=c
Putting that into the most general form will still not be much help until you have values for h and v.
'
hv-2vx-2hx%2B4x%5E2-c=0
4x%5E2-2%28v%2Bh%29x%2Bhv-c=0
'
x=%282%28v%2Bh%29%2Bsqrt%284%28v%2Bh%29%5E2-4%2A4%28hv-c%29%29%29%2F%282%2A4%29 or (ignoring the "negative" square root x=()/())
highlight%28x=%28%28v%2Bh%29%2Bsqrt%28%28v%2Bh%29%5E2-4%28hv-c%29%29%29%2F%284%29%29
Be sure that hv%3E=0.