The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms?

Options

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

Answer

C

Explanation

Let the side of an equilateral triangle be x cm.
`therefore` Area of equilateral triangle, `A=sqrt(3)/4 x^(2)` …………………(i)
Also, `(dx)/(dt)`=2cm/s
On differentiating Eq. (i), w.r.t. t, we get
`(dA)/(dt)= sqrt(3)/4. 2x.(dx)/(dt)`
`=sqrt(3)/4.2.10.2` `[therefore x=10 "and" (dx)/(dt)=2]`
`=10sqrt(3)cm^(2)//s`