SOLUTION: An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. F

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Question 115523: An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
:
There are many dimensions that will satisfy this requirement.
:
Let x = width; y = length of the rectangular piece tin
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We know the height will be 2inches, then the base will = 100/2 = 50 sq/in
:
The base dimension will be (x-4) by (y-4)
:
write an equation where y is the length and x = width
:
(x-4)(y-4) = 50
FOIL
xy - 4y - 4x + 16 = 50
:
xy - 4y = 50 + 4x - 16
:
y(x-4) = 4x + 34
:
y =%28%284x%2B34%29%29%2F%28%28x-4%29%29
:
With this equation you can substitute any value greater than 4 for x (width)
y = length for that width which will give you 100 cu inches
:
Sticking to integers: let x = 9"
:
y = %284%289%29%2B34%29%29%2F%28%289-4%29%29
y = 70%2F5
y = 14"
;
Check the box dimensions: (14-4)*(9-4)*2 = 100 cu in
:
Let x = 29"
y = %284%2829%29%2B34%29%29%2F%28%2829-4%29%29
y = %28%28116%2B34%29%29%2F25
y = 6"
:
Check box dimensions: (29-4)*(6-4)*2 = 100 cu in