Delhi Police Constable Exam Model Paper 3

GIVEN:
Area of equilateral triangle = $36\sqrt{3}\mathit{c}{\mathit{m}}^2$
CONCEPT:
Mensuration
FORMULA USED:
Area of equilateral triangle $=\frac{\sqrt{3}}{4}{\mathit{a}}^2$
Length of median of equilateral triangle = $\frac{\sqrt{3}\mathit{a}}{2}$
CALCULATION:
Let side of triangle = a
Now,
$\frac{\sqrt{3}}{4}{\mathit{a}}^2=36\sqrt{3}$
⇒ ${\mathit{a}}^2=144$
⇒ a = 12
∴ Length of median = $\frac{\sqrt{3}\mathit{a}}{2}=6\sqrt{3}=6\sqrt{3}$ cm