question_answer

In a\[\Delta ABC,G\]is the centroid. What is the ratio of area of \[\Delta AGC\]to area of\[\Delta ABC?\]

A)  1 :2                            

B)  1 :3                

C)  1:4                 

D)    1:6

Correct Answer: B

Solution :

ar of \[\Delta AGB=ar\,of\,\Delta BGC=ar\]of \[\Delta AGC\] \[\Rightarrow \]\[3[\Delta AGC]=\Delta ABC\] \[\Rightarrow \]\[\frac{\Delta \Alpha GC}{\Delta ABC}=\frac{1}{3}=1:3\]