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Question
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 ?
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.
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