A) Isosceles triangle
B) Equilateral triangle
C) Scalene triangle
D) None of these
Correct Answer: B
Solution :
Let \[A\,(0,\,0),\,B\,(a,\,\,0)\] and \[C\,\left( \frac{a}{2},\,\frac{a\sqrt{3}}{2} \right)\] Hence\[AB=\sqrt{{{a}^{2}}+0}=a,\,\,BC=\sqrt{{{\left( \frac{a}{2} \right)}^{2}}+{{\left( \frac{a\sqrt{3}}{2} \right)}^{2}}}=a\] and \[AC=\sqrt{{{\left( \frac{a}{2} \right)}^{2}}+{{\left( \frac{a\sqrt{3}}{2} \right)}^{2}}}=a\] Hence the triangle is equilateral.
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