SOLUTION: From each corner of a square piece of sheet metal, remove a square of side 9 centimeters. Turn up the edges to form an open box. If the box is to hold 144 cubic centimeters, what s

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Question 1010066: From each corner of a square piece of sheet metal, remove a square of side 9 centimeters. Turn up the edges to form an open box. If the box is to hold 144 cubic centimeters, what should be the dimensions of the piece of sheet metal?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Unknown side length of the square, x.
Known height created by the "edges" or flaps to be folded, h.
The volume of the resulting box is known, v.

The assigning of variables, system%28x=unknown%2Ch=9%2Cv=144%29.

Multiply the three dimensions of the resulting box gives the specified volume.
This equation comes from the description:
highlight_green%28h%28x-2h%29%28x-2h%29=v%29


NOTE: UNKNOWN MISTAKE IN THE GENERALIZED SYMBOLIC SOLUTION; SEE THE MORE SPECIFIC STEPS BELOW.
Solve for the unknown variable,x.
h%28x%5E2-4hx%2B4h%5E2%29-v=0
hx%5E2-4hx%2B4h%5E3-v=0
Depending on comfort and how long you want to continue all in symbols, substitute the given values any time.

x=%284h%2B-+sqrt%28%28-4h%29%5E2-4%2Ah%284h%5E3-v%29%29%29%2F%282h%29

x=%284h%2B-+sqrt%2816h%5E2-4h%5E4%2B4hv%29%29%2F%282h%29

x=%284h%2B-+2sqrt%284h%5E2-h%5E4%2Bhv%29%29%2F%282h%29

x=%282h%2B-+sqrt%284h%5E2-h%5E4%2Bhv%29%29%2Fh
Certainly, substitute the given values now at the latest, and evaluate x.
Finding imaginary component to the solution, so must be a mistake (maybe on my part).


*MORE SPECIFIC, DIRECTLY USING THE GIVEN VALUES WITHOUT GENERALIZATIONS:
Trying again without generalizing:
9%28x-2%2A9%29%28x-2%2A9%29-144=0
%28x-18%29%5E2-16=0
%28x-18%29%5E2=16
x-18=0%2B-+4
x=18%2B-+4
Subtracting 4 will not work for anything realistic. Use the PLUS form.
highlight%28x=22%29.