How to fit 5 samesize squares into 1 bigger square

Coen van Baalen

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Dec 28, 2017
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Hello,

I've got stuck on this problem where you have 5 squares of the same size which have to make 1 bigger square together. You're only allowed to cut every square 1 time and you have to use all of the materials of the 5 small ones in the bigger one.

Thanks you for your help!
 
We would be delighted to see your efforts.

Small Note: 5 * 1x1 = 5
Large Note: 1 * \(\displaystyle \sqrt{5}\cdot\sqrt{5}\) = 5

If you need sides that lead to a square area of 5, and if it can be done, it will take a more creative solution than just cutting willy-nilly.
 
Take four of the squares. For each, cut from the midpoint of one side to an opposite corner. Arrange the four larger pieces symetrically so that each has a side adjacent to a side of the uncut piece. The four smaller pieces will fill the corners of the large required square.
 
...and guess what that cut gives you.
 
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