Question

The median of an equilateral triangle is increasing at the ratio of ${\displaystyle 2\sqrt{3}}$ cm/s. Find the rate at which its side is increasing.

Answer 1

Let ‘a’ be the side of an equilateral triangle.

Medain AM = ${\displaystyle \frac{\sqrt{3}}{2}a}$

Given ${\displaystyle \frac{d\left(AM\right)}{dt}=2\sqrt{3}}$ cm/s

${\displaystyle \frac{d\left(AM\right)}{dt}=\frac{d\left(\frac{\sqrt{3}}{2}a\right)}{da}\times \frac{da}{dt}}$

${\displaystyle 2\sqrt{3}=\frac{\sqrt{3}}{2}.\frac{da}{dt}}$

${\displaystyle \Rightarrow \frac{da}{dt}}$ = 4 cm/s