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Question
The median of an equilateral triangle is increasing at the ratio of `2sqrt(3)` cm/s. Find the rate at which its side is increasing.
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Solution
Let ‘a’ be the side of an equilateral triangle.
Medain AM = `sqrt(3)/2a`
Given `(d(AM))/(dt) = 2sqrt(3)` cm/s
`(d(AM))/(dt) = (d(sqrt(3)/2a))/(da) xx (da)/dt`
`2sqrt(3) = sqrt(3)/2 . (da)/dt`
`\implies (da)/dt` = 4 cm/s
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