A) \[~20\text{ }c{{m}^{2}}\]
B) \[~5\text{ }c{{m}^{2}}\]
C) \[~30\text{ }c{{m}^{2}}\]
D) \[10c{{m}^{2}}\]
Correct Answer: D
Solution :
Ad is the median of \[\Delta \Alpha \Beta C\] \[\therefore \]Area of \[\Delta \Alpha \Beta D=\]Area of \[\Delta \Alpha DC\] ?(i) Also, Ed becomes the median of\[\Delta \Beta \Epsilon C\] \[\therefore \]Area of\[\Delta \Beta \Epsilon D=\]Area of \[\Delta \Epsilon CD\] ?(ii) Subtracting (i) & (ii) Area \[(\Delta \Alpha \Beta D-\Delta BED)=Area(\Delta \Alpha DC-\Delta ECD)\] \[\Rightarrow \]Area \[(\Delta \Alpha \Beta \Epsilon )=Area(\Delta \Alpha \Epsilon C)\] Hence, Area \[(\Delta \Alpha \Beta \Epsilon )=Area(\Delta AEC)=10c{{m}^{2}}\]You need to login to perform this action.
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