ΔABC is an equilateral triangle and AD ⊥ BC, where D lies on BC. If AD = $4\sqrt{3}$ cm, then what is the perimeter (in cm) of ΔABC ?

24

We know that,

Length of perpendicular bisector = length of median, AD = \(\frac{\sqrt {3}}{2}\) × side

= 4\(\sqrt {3}\) = \(\frac{\sqrt {3}}{2}\) × side  

= side = 4\(\sqrt {3}\) × \(\frac{2}{\sqrt {3}}\)

= side = 8 cm

So perimeter of triangle = 8 × 3 = 24 cm