A) \[20\sqrt{7}\,c{{m}^{2}}\]
B) \[10\sqrt{14}\,c{{m}^{2}}\]
C) \[20\sqrt{14}\,c{{m}^{2}}\]
D) \[140\,c{{m}^{2}}\]
Correct Answer: C
Solution :
Let the sides of \[\Delta \Alpha \Beta C\]be a, b, c Then, \[(s-a)=8,(s-b)=7\]and \[(s-c)=5\] \[\Rightarrow \]\[(s-a)+(s-b)+(s-c)=20\] \[\Rightarrow \]\[(s-a)+(s-b)+(s-c)=20\] \[\Rightarrow \]\[3s-(a+b+c)=20\] \[\Rightarrow \]\[3s-2s=20\] \[\Rightarrow \]\[s=20\] \[\left[ \because \,s=\frac{a+b+c}{2} \right]\] \[\therefore \]Area of \[\Delta \Alpha \Beta C=\sqrt{20\times 8\times 7\times 5}\] \[=\sqrt{5600}\,c{{m}^{2}}=20\sqrt{14}\,c{{m}^{2}}\]
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