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The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ? - Mathematics

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The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?

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Solution

Area of an equilateral triangle, `A = sqrt3/4 a^2`

where 

a = Side of an equilateral triangle

Given:

`(da)/(dt)` =2 cm/s

Now,

`(dA)/(dt)=d/dt(sqrt3/4a^2)`

`=sqrt3/4 xx 2 xx a xx(da)/(dt)`

`=(sqrt3a)/2xx(da)/(dt)`

`=(sqrt3a)/2xx2`

`=sqrt3a` cm2/s

`therefore [(dA)/(dt)]_(a=20)=20sqrt3` cm2/s

Hence, the area is increasing at the rate of `20sqrt3` cm2/s when the side of the triangle is 20 cm.

Concept: Increasing and Decreasing Functions
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