Question

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.

Answer 1

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

Area of equilateral Δ^le = A = \(\frac{\sqrt3}{4}\)x² 

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

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