In triangle PQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD ?

A. $$\frac{{4\sqrt {86} }}{3}$$

B. $$\frac{{2\sqrt {86} }}{3}$$

C. $$\frac{{5\sqrt {86} }}{3}$$

D. $$\frac{{5\sqrt {86} }}{2}$$

Answer: Option A

Solution (By Examveda Team)

(PQ)² + (PR)² = 2(QD² + PD²)
(30)² + (50)² = 2[(18)² + PD²]
900 + 2500 = 2[324 + PD²]
3400 = 2[324 + PD²]
1700 = 324 + PD²
PD² = 1376
PD = $$4\sqrt {86} $$
CD = $$\frac{1}{3}$$PD
CD = $$\frac{{4\sqrt {86} }}{3}$$