The points A(k,2k−1), B(3k−4,k+5) and C(7,k) form a triangle whose area is 20 square units.
a. (i) Set up the equation in k that results from the given area condition and simplify it to a quadratic equation.
b. (ii) Solve the quadratic equation to obtain all real values of k.
c. (iii) For each value of k obtained, determine whether triangle ABC is acute-angled, right-angled or obtuse-angled by examining the squares of its side lengths.