A) \[24\sqrt{3}\,cm\]
B) \[24\,\,cm\]
C) \[36\,\,cm\]
D) \[27\,\,cm\]
Correct Answer: A
Solution :
Let ABC be an equilateral triangle whose perpendiculars OD, OE and OF are 10 cm. 12 cm. and 14 cm respectively. Let the side of equilateral triangle AB, BC and AC = a cm. \[\therefore \] Area of \[\Delta \,ABC=\frac{1}{2}\times AB\times OD+\frac{1}{2}\] \[\times AC\times OF+\frac{1}{2}\times BC\times OF\] \[\Rightarrow \,\,\,\frac{\sqrt{3}}{4}\times {{a}^{2}}=\frac{1}{2}\times a(OD+OE+OF)\] \[(\because \,\,AB=BC=AC=a\,cm)\] \[\Rightarrow \,\,\,\frac{\sqrt{3}}{4}\times {{a}^{2}}=\frac{a}{2}\,(10+12+14)\] \[\Rightarrow \,\,\frac{\sqrt{3}}{4}\times {{a}^{2}}=\frac{a}{2}\times 36\Rightarrow \frac{\sqrt{3}}{2}a=36\] \[\therefore \,\,\,\,a=\frac{36\times 2}{\sqrt{3}}=\underline{\mathbf{24}\sqrt{\mathbf{3}}\,\mathbf{cm}}\]You need to login to perform this action.
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