I think you would use the Pythagorean Theorem to solve this, as a square cut across diagonally creates two isocele triangles. Since the longest side is 20 m, this value would be imputed into c^2.
a^2 + b^2 = c^2
a^2 + a^2 = 20^2
2a^2 = 400
2a^2/2 = 400/2
a^2 = 200
a = 14.14
Thus, each sides of the playground are 14.14 meters long.
