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A square is divided into four congruent rectangles and a smaller square, as shown.


Square divided into four congruent rectangles and a smaller square

The area of the small square is ${\frac{1}{4}}$ of the area of the whole square.

What is the ratio of the length of a short side of one of the rectangles to the length of a long side?


 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.