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What is the ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half (as shown below) is similar to the original rectangular sheet? Express your answer as a common fraction in simplest radical form. (Assume the width of the original sheet of paper becomes the length of the folded sheet.)
 

 Sep 18, 2015
 #1
avatar+129852 
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Let W be the original width and L be the original length

 

After folding we have  the new  width = (1/2)L  and the new length = W

 

So

 

L /W = W / (1/2)L   cross-multiply

 

(1/2)L^2  = W^2      take the square root of both sides

 

sqrt(1/2)L = W

 

sqrt(2)/2   = W / L

 

I don't see any diagram, Mellie.....so I'm just guessing at the answer, here.....!!!!!

 

 

cool cool cool

 Sep 19, 2015

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