Question

Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square increasing when the area of the square is 16cm^(2). Show step-by-step solution

Answer 1

Area of a square = length²
A = x²
16 = x²; x = 4
dA/dx = 2x cm²/s
dx/dt = 6 cm/s
Using chain rule:
dA/dt = dA/dx * dx/dt
dA/dt = 2x * 6
dA/dt = 12x
At x = 4,
dA/dt = 12(4) = 48 cm²/s