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

Options

A. `10sqrt(2)cm^(2)//sec`
B. `10sqrt(3)cm^(2)//sec`
C. `10 cm^(2)//sec`
D. `5cm^(2)//sec`

Answer

B

Explanation

Let x be the side and A be the area of equilateral triangle at time t. Then,
`A=(sqrt(3))/(4)x^(2)`
`implies(dA)/(dt)=sqrt(3)/(2)xx(dx)/(dt)`
`implies(dA)/(dt)=(sqrt(3))/(2)xx10xx2=10sqrt(3)" "[because x=10 and (dx)/(dt)=2]`