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A square is divided into four congruent rectangles and a smaller square, as shown.
(The diagram is not to scale.)

Square divided into four congruent rectangles and a smaller square

The area of the small square is 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.