Question

The side of an equilateral triangle expands at the rate of $\sqrt{3}cm/sec$.When the side is $12cm$, the rate of increase of its area is ______

• A. $12{cm}^2/sec$
• B. $18{cm}^2/sec$
• C. $3\sqrt{3}{cm}^2/sec$
• D. $10{cm}^2/sec$

Answer 1

Answer: (B)

$18{cm}^2/sec$

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

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

$\frac{dA}{dt}=\frac{\sqrt{3}}{2}\times 12\times \sqrt{3}c{m}^2/s$

$=18c{m}^2/s$