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What they are getting at is how that was possible while still maintaining a 5 x 13 triangle.

At a glance any arrangement within the 5x13 should fill up all available space.
 
The hypoteneuses of the two triangles are different - if you were to superimpose the triangles you would see that the upper one is actually smaller because of the angle - the missing square.
 
Okay, this is why I never did work in any of my math classes... What I would do was fill in the blank square with my pen, and hand it in.
 

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