question_answer

In a triangle, distances from centroid to vertices are respectively 4 cm, 6 cm and 8 cm. Find medians.

A)  16 cm, 4 cm, 18 cm

B)  4 cm, 6 cm, 8 cm

C)  6 cm, 9 cm, 12 cm

D)  20 cm, 21 cm, 25 cm

Correct Answer: C

Solution :

Given that, AO = 4 cm, BO = 6 cm, CO = 8 cm O is centroid (intersection point of median). Then,    \[\frac{AO}{OF}=\frac{2}{1}\Rightarrow \frac{AO}{2}=OF\] \[\Rightarrow \,\] \[OF=\frac{4}{2}=2\,\,cm\] Similarly, OD = 3 cm and OE = 4 cm Now length of median AF = (AO+ OF) = (4 + 2) = 6 cm BD = (BO+OD) = (6+3) = 9 cm CE = (CO + OE) = (8 + 4) = 12 cm