Competing Squares

competing squares

A square has been inscribed in each of two congruent isosceles right triangles. Which square is larger?

	Select Click for Answer
Divide each figure into a grid of triangles. This shows that the square on the left occupies 2/4 of its triangle, while the square on the right occupies 4/9 of its triangle. So the square on the left is about 12.5 percent larger. (Duane Detemple and Sonia Harold, “A Round-Up of Square Problems,” Mathematics Magazine 69:1 [February 1996], 15-27.)