question_answer

Triangle ABC has vertices (0, 0), (11, 60) and (91, 0). If the line\[y=kx\]cuts the triangle into   2 two triangles of equal area, then k is equal to

A)  \[\frac{30}{51}\]                                             

B)  \[\frac{4}{7}\]

C)  \[\frac{7}{4}\]                  

D)         \[\frac{30}{91}\]

E)  \[\frac{27}{37}\]

Correct Answer: A

Solution :

As the line divides the\[\Delta ABC\]in equal area. Midpoint of AB(51, 30) which lies on\[y=kx\] \[\therefore \]  \[30=51k\Rightarrow k=\frac{30}{51}\]