The sides are given, so we need maximum values for diagonals.

Draw diagonals $AC, CE, EA$ and we get 3 isosceles triangles. H is a point on AC such that, BH and AC are perpendicular. The maximum value BE can get is EH+BH (for a triangle sum of two sides is greater than 3rd) and it's only possible if ABCE is a kite, so AE=EC.

Do it for other diagonals (DE, FA) and you will get the answer.