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

Question

Jovanni

Mathematics

14 June, 06:40

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

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Caitlin Bowers · 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