A) \[48\sqrt{3}\,c{{m}^{2}}\]
B) \[54\sqrt{3}\,c{{m}^{2}}\]
C) \[72\sqrt{3}\,c{{m}^{2}}\]
D) \[80\sqrt{3}\,c{{m}^{2}}\]
Correct Answer: A
Solution :
Let the side of the equilateral triangle be x cm. \[\therefore \] \[\Delta AOB+\Delta BOC+\Delta COA=\Delta ABC\] \[\Rightarrow \] \[\frac{1}{2}x\times 3+\frac{1}{2}\times x\times 4+\frac{1}{2}\times x\times 5\] \[=\frac{\sqrt{3}}{4}{{x}^{2}}\] \[\Rightarrow \] \[6=\frac{\sqrt{3}}{4}x\] \[\Rightarrow \] \[x=\frac{24}{\sqrt{3}}=8\sqrt{3}\] \[\therefore \] Area of \[\Delta ABC=\frac{\sqrt{3}}{4}\times sid{{e}^{2}}\] \[=\frac{\sqrt{3}}{4}\times 8\sqrt{3}\times 8\sqrt{3}=48\sqrt{3}\] sq cmYou need to login to perform this action.
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