Square Ratio

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
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Problem



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

Image
Square Ratio


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.