The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $50\sqrt{3}\, cm^2/sec$
$\text{Let side of the equilateral triangle be }a$
$\text{Area }A=\frac{\sqrt{3}}{4}a^{2}$
Given: $\frac{da}{dt}=5\text{ cm/s}$
$\frac{dA}{dt}=\frac{\sqrt{3}}{4}\times2a\frac{da}{dt}=\frac{\sqrt{3}}{2}a\frac{da}{dt}$
When $a=20$:
$\frac{dA}{dt}=\frac{\sqrt{3}}{2}\times20\times5=50\sqrt{3}$
$\frac{dA}{dt}=50\sqrt{3}\ \text{cm}^2/\text{s}$