A) \[m\text{/}n\]
B) \[{{\left( m\text{/}n \right)}^{2}}\]
C) \[{{\left( n\text{/}m \right)}^{2}}\]
D) \[{{\left[ m/{{(n+m)}^{2}} \right]}^{2}}\]
Correct Answer: D
Solution :
(d):- In \[\Delta AFD\] and \[\Delta FEB\] \[\angle AFD=\angle BFE\] (Vertically opposite angles) And \[\angle ADC=\angle ABC\] \[\therefore \] \[\Delta AFD\tilde{\ }\Delta BFE\] So, \[\frac{ar\left( \Delta FED \right)}{ar\left( \Delta AFD \right)}=\frac{E{{B}^{2}}}{A{{D}^{2}}}=\frac{{{m}^{2}}}{{{\left( mn \right)}^{2}}}\] \[=\frac{{{m}^{2}}}{{{\left( mn \right)}^{2}}}={{\left[ \frac{m}{m+n} \right]}^{2}}\]
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