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Question:

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

Solution:

let A = area and a = side
A = √3a²/4
By chain rule:
dA/dt = dA/da × da/dt = √3a/2 × da/dt
a = 20cm, da/dt = 2cm/s
⇒ dA/dt = 20√3 cm²/s