Question

The sides of an equilateral triangle are increasing at the rate of $2cm/sec$. Find the rate at which its area increases, when side is $10cm$ long.

Answer 1

Given the sides the equilateral triangle$=a$cm.

Area of te equilateral triangle$A=\frac{\sqrt{3}}{4}{a}^2$

Differentiating w.r.t $t$ we get

$\frac{dA}{dt}=\frac{\sqrt{3}}{4}2a\frac{da}{dt}$

But it is given that $\frac{da}{dt}=2cm$per sec.

When $a=10$cm

$\therefore \frac{dA}{dt}=\frac{\sqrt{3}}{4}\times 2\times 10\times 2=10\sqrt{3}{cm}^2$per second