The vertices of triangle PQR are P(1,4), Q(5,−2) and R(−3,−2).
a. (i) Calculate the lengths of all three sides PQ, QR and RP.
b. (ii) Verify whether triangle PQR is right-angled.
c. (iii) Further, classify triangle PQR as equilateral, isosceles or scalene, giving reasons for your classification.