An equilateral ΔABC has AD as its median. Find the length of OD where ‘O’ is the centroid if the area of the triangle is √3 cm2. एक समबाहु त्रिभुज ΔABC की माध्यिका AD है | OD की लम्बाई ज्ञात कीजिये, जहाँ ‘O’ केन्द्रक है, यदि त्रिभुज का क्षेत्रफल √3 सेमी2 है|

Area of equilateral triangle = (√3/4) × side². Given area = √3, so (√3/4) × a² = √3. Dividing by √3: a²/4 = 1, so a² = 4 and a = 2 cm. In equilateral triangle, median = altitude = (√3/2) × side = (√3/2) × 2 = √3 cm. Centroid divides median in ratio 2:1 (vertex to centroid : centroid to midpoint). OD = (1/3) × AD = (1/3) × √3 = 1/√3 cm.