Question

The side of an equilateral triangle is increasing at the rate of 2 cm/sec. At what rate is its area increasing when the side of the triangle is 20 cm ?

Answer 1

At any time t, let x cm be the length of a side of an equilateral triangle and A be its area. Then,

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

$\frac{dA}{dt}=\frac{\sqrt{3}}{4}\times 2x\times \frac{dx}{dt}$

$(\frac{dA}{dt}{)}_{x=20}=\frac{\sqrt{3}}{2}\times 20\times 2=20\sqrt{3}c{m}^2\sec$