Pythagorean theorem. I.e., the large square is on the hypotenuse of the right triangles (which are all the same shape and size), and the other two squares are on the two legs. A little thought shows that the sum of the squares of the legs have the same area as the square of the hypotenuse. There are 96 other proofs here.
He decided to use the same fabrics, so it would look more coordinated when both pillows are sitting on the couch together.
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