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Question

Side of an equilateral triangle expands at the rate of $$2 cm/sec$$. The rate of increase of its area when each side is $$10cm$$ is


A
102cm2/sec
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B
103cm2/sec
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C
10cm2/sec
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D
5cm2/sec
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Solution

The correct option is B $$10 \sqrt 3 cm^2 /sec$$
Given $$\dfrac{dx}{dt}=2cm/sec,x=10cm$$

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

$$ \Rightarrow \displaystyle \frac {dA}{dt} = \displaystyle \frac{ \sqrt 3} {2} x \frac {dx}{dt} $$

$$ \Rightarrow \displaystyle \frac{dA}{dt} = 10\sqrt{3} cm^{2}/sec$$ 

Mathematics

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