In ΔABC, X is the centroid of the triangle. If AP + QC + BR = 9 cm then find the perimeter of ΔABC. (Diagram not drawn to scale.)

X is the centroid of ΔABC, so the cevians AR, BQ, CP are MEDIANS. Hence P, Q, R are the midpoints of sides AB, AC, BC respectively. Therefore: - AP = AB/2 (P is midpoint of AB) - QC = AC/2 (Q is midpoint of AC) - BR = BC/2 (R is midpoint of BC) Sum: AP + QC + BR = (AB + AC + BC)/2 = perimeter / 2. Given AP + QC + BR = 9 cm ⇒ perimeter = 2 × 9 = 18 cm. Answer: option 3) 18 cm.