If f : R→N∪{0}, where f(area of triangle joining points P(5, 0), Q(8,4) and R(x, y) such that angle PRQ is a right angle) = number of triangles, then which of the following is true?

Since ∠PRQ=π/2 and points P, Q, R lie on the circle with PQ as diameter.Also, PQ = 5.Now, the maximum area of the triangle isΔmax=12(5)52=6.25For area = 5, we have four symmetrical positions of point R(shown as R1, R2, R3, R4).For area = 6.25, we have exactly two points.For area = 7, no such points exist.