Let G(p,p), H(5,2) and J(3,p+4) be the vertices of a triangle.
a. (i) Derive the quadratic equation satisfied by p if the area of triangle GHJ is 7.5 square units.
b. (ii) Solve the quadratic equation obtained in part (i) and list all real values of p.
c. (iii) For each permissible value of p, state whether the triangle GHJ is isosceles, scalene or right-angled, giving reasons based on side lengths.