SOLUTION: A rectangular piece of tin is twice as long as it is wide. A 2 inch square is cut out of each corner, and the sides are turned up to make a box with an open top. The volume of the
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Question 34408: A rectangular piece of tin is twice as long as it is wide. A 2 inch square is cut out of each corner, and the sides are turned up to make a box with an open top. The volume of the box is 480 in^3. Find the original dimensions of the piece of tin.
Length:
Width: Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! The piece of tin is x by 2x inches. After cutting out the 2 inch corners the tin is now length is(x-4)& the width is (2x-4)and the height is 2 so the volume is
(x-4)(2x-4)2=480 or (x-4)(2x-4)=240 (divided both sides by 2) or
2x~2-12x+16-240=0 (subtracted 240 from both sides) or
2x~2-12x-224=0 now dividing all terms by 2 yields x~2-6x-112=0 now factoring this equation we get (x+8)(x-14)=0 or x=-8 or x=14 the positive solution is the only one that fits the problem.
Therefore the original dimensions were 14 & 28 or x-4=10 & 2x-4=24 and the hight is 2 thus 10*24*2=480in~3
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