Question 815942: I am really stuck can some please help me with this word problem..Another rectangular piece of sheet metal is 2 in. longer than it is wide. A square piece 3 in. on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 765 in.^3. Find the dimensions of the original piece of metal.
Thank you :)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Another rectangular piece of sheet metal is 2 in. longer than it is wide.
A square piece 3 in. on a side is cut from each corner.
The sides are then turned up to form an uncovered box of volume 765 in.^3.
Find the dimensions of the original piece of metal.
:
Let L = length of the original metal
Let W = Width of it
"piece of sheet metal is 2 in. longer than it is wide", therefore:
L = W+2
:
When 3" squares are cut from all 4 corners, the dimension of the box:
(L-6) by (W-6) by 3
Replace L with (W+2) and write the volume equation
((W+2)-6) * (W-6) * 3 = 765
(W-4) * (W-6) * 3 = 765
FOIL
(W^2 - 6W - 4W + 24)*3 = 765
Simplify, divide both sides by 3
W^2 - 10W + 24 = 255
W^2 - 10W + 24 - 255 = 0
W^2 - 10W - 231 = 0
You can us the quadratic formula, but this will factor
(W+11)(W- 21) = 0
The positive solution is all we want here
W = 21 inches is the width of the original piece metal
then
L = 21 + 2 = 23 inches is the Length
:
:
See if that checks out, find the vol with these value (subtract 6 from the length and width)
17 * 15 * 3 = 765
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