The side of an equilateral triangle is increasing at the rate √3 cm./sec.

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The side of an equilateral triangle is increasing at the rate √3 cm./sec. Find the rate at which its area is increasing when its side is 2 meters.

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Given $\frac{dx}{dt}$ = √3cm/sec., x = 2 meters, $\frac{dA}{dt}$ = ?

Area of equilateral Δle = A = $\frac{\sqrt3}{4}$x2

$\frac{dA}{dt}$ = $\frac{\sqrt3}{4}$.2x$\frac{dx}{dt}$

= $\frac{\sqrt3}{4}$. 2. 200. √3 = 300cm2/sec.