Applications Of Derivatives Question 166
Question: The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is
[Kerala (Engg.) 2002]
Options:
A) $ \sqrt{3} $ sq. unit/sec
B) 10 sq. unit/sec
C) $ 10\sqrt{3} $ sq. unit/sec
D) $ \frac{10}{\sqrt{3}} $ sq. unit/sec
Show Answer
Answer:
Correct Answer: C
Solution:
If x is the length of each side of an equilateral triangle and A is its area, then $ A=\frac{\sqrt{3}}{4}x^{2}\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{4}2x\frac{dx}{dt} $ Here, $ x=10cm $ and $ \frac{dx}{dt}=2cm/sec $
therefore $ A=10\sqrt{3} $ Sq. unit per sec.
BETA
