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 3 years ago
The area of the paper is 260 in2.
Then 2 inch square is cut from each corner and folded up to make a box.
The volume of the box is 288 in3
what are the dimensions of the paper for this to be true?
How do i do this?
 3 years ago
The area of the paper is 260 in2. Then 2 inch square is cut from each corner and folded up to make a box. The volume of the box is 288 in3 what are the dimensions of the paper for this to be true? How do i do this?

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robtobey
 3 years ago
Best ResponseYou've already chosen the best response.0Let x and y be the width and length of the uncut paper respectively. The area is given to be 260 sq inches, so\[x* y=260\]The length of the box width is x2*2 because there are two each 2x2 inch squares cut out of each corner to make the box. The length of the box length is y2*2 for the same reason. The box height will be 2 inches. The volume, 288 cubic inches, is equal to the product of the width*length*height or\[2(x2*2)(y2*2)= 288\]Solving the two simultaneous for x and y yields:\[\{x\to 13,y\to 20,x\to 20,y\to 13\} \]The uncut paper is 13 by 20 inches.

tdabboud
 3 years ago
Best ResponseYou've already chosen the best response.0how did you solve them simultaneously?

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.0x*y=260, y=260/x Replace y in the other equation with 260/x\[2(x2*2)(y2*2)=288\]\[2(x2*2)\left(\frac{260}{x}2*2\right)=288 \]\[552\frac{2080}{x}8 x288=0\]Multiply each side by x and combine the resulting fractions.\[x\left(552\frac{2080}{x}8 x288\right)= 0*x\]\[8 \left(26033 x+x^2\right)=0\]\[260  33 x + x^2 = 0 \]Use the binomial theorem or factor the LHS.\[(x13)(x20) =0 \]x=13 is the answer you want. Use y=260/x to find the corresponding y.
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