| In fig. \[\left. MN \right\|BC\] and \[\text{AM}:\text{MB}=\text{1}:\text{2},\]then \[\frac{ar(\Delta AMN)}{ar(\Delta ABC)}\] is: |
 |
A) \[1:4\]
B) \[1:9\]
C) \[1:1\]
D) \[1:2\]
Correct Answer: B
Solution :
| [b] Here, \[\Delta AMN\tilde{\ }\Delta ABC\] |
| \[\therefore \,\,\,\frac{ar(\Delta AMN)}{ar(\Delta ABC)}=\frac{{{(AM)}^{2}}}{{{(AB)}^{2}}}=\frac{{{(AM)}^{2}}}{{{(AM+MB)}^{2}}}\] |
| \[=\frac{{{k}^{2}}}{{{(k+2k)}^{2}}}=\frac{{{k}^{2}}}{9{{k}^{2}}}=\frac{1}{9}\] |
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