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