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In a square of side length 40, can we fit a 10 x 45 rectangle?

 

Note: You cannot fold / break the rectangle or the square.

 

 Dec 16, 2019
 #1
avatar+22114 
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Yes, it will fit diagonally....

 Dec 16, 2019
 #2
avatar+109748 
+1

As EP  pointed out, it will fit diagonally...

 

Let the bottom left vertex of the square   be located at  (0,0)

 

And the two  vertexes  of the short side of the rectangle  can be  located at  (0, 10/√2)  and  ( 10/√2, 0)

 

And let the other two  vertexes  be located at   (40 - 10/√2, 40)  and ( 40, 40 - 10/√2)

 

And  the distance  between     (10/√2, 0 )   and  ( 40 , 40 - 10/√2)  =

 

√ [ (40 - 10/√2)^2   + (40 - 10/√2)^2 ]  =   √2 * (40 - 10/√2)  = 40√2 - 10   ≈  46.56  

 

So.....the rectangle will fit

 

 

 

cool cool cool

 Dec 17, 2019

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