If f:R→N∪0, where f (area of triangle joining points P5,0, Q8,4  and  Rx,y such that angle PRQ is a right angle) = number of triangles, then which of the following is true?

Hence   ∠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=12552=6.25For area = 5, we have four symmetrical positions of pointRshown   as   R1,R2,R3,R4.For area = 6.25, we have exactly two points.For area: 7 , no such points exist.