Question

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

Answer 1

Let the side of triangle be a.

$\frac{da}{dt}=2cm/sec.$

Now, area of equilateral triangle having side a is given by

$A=\frac{\sqrt{3}{a}^2}{4}$

On differentiating w.r.t. t, we get,

$\frac{dA}{dt}=\frac{\sqrt{3}}{4}\left(2a\right)\frac{da}{dt}$

$\frac{dA}{dt}=\frac{\sqrt{3}}{4}\times 2\times 10\times 2=10\sqrt{3}c{m}^2/sec.$