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The sides of an equilateral triangle ar...

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec . The rate of which its area increases, when side is 10 cm, is

A

`sqrt3` sq. unit/sec

B

10 sq. unit/sec

C

`10sqrt3` sq. unit/sec

D

`(10)/(sqrt3)` sq. unit/sec

Text Solution

Verified by Experts

The correct Answer is:
C
If x is the length of each side of an equilateral triangle and A is
its area, then`A=(sqrt(3))/(4)x^(2)implies(dA)/(dt)=(sqrt(3))/(4)2x(dx)/(dt)`
Here, `x=10cm` and `(dx)/(dt)=2(cm)/(sec)`
`impliesA=10sqrt(3)sq`. Unit per sec.
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