# Problem 583: Heron Envelopes
A standard envelope shape is a convex figure consisting of an isosceles
triangle (the flap) placed on top of a rectangle. An example of an
envelope with integral sides is shown below. Note that to form a
sensible envelope, the perpendicular height of the flap (BCD) must be
smaller than the height of the rectangle (ABDE). In the envelope
illustrated, not only are all the sides integral, but also all the
diagonals (AC, AD, BD, BE and CE) are integral too. Let us call an
envelope with these properties a Heron envelope. Let S(p) be the sum of
the perimeters of all the Heron envelopes with a perimeter less than or
equal to p. You are given that S(104) = 884680. Find S(107).