The side of an equilateral triangle decreases at the rate of 2 cm/s. At what rate is the area decreasing when the area is 100 cm2?

Question

I need help with the following question:

The side of an equilateral triangle decreases at the rate of 2 cm/s. At what rate is the area decreasing when the area is 100 cm2?

Answer 1

A = √3s²/4 , ds/dt = -2 , √3s²/4 = 100 --> s² = 400/√3 and s = 20 / ⁴√3

dA/dt = (√3s / 2) · ds/dt = -20/√3