# Each side of a square is increasing at a rate of 6 cm/s . At what rate is the area of the square increasing when the area of the square is 16 cm^{2} ?

**Solution:**

Given each side of the __square__ is increasing at a rate of 6cm/s

__Area__, A = s^{2}

s is the side length

=> (dA)/(dt)

= (dA/ds)*(ds/dt)

= 2s*(ds)/(dt) {__chain rule__ of differentiation}

(ds)/(dt) = 6 cm/s

When A = 16 cm^{2}

=> 16 = s^{2}

=> s = √(16)

=> s = 4 cm

Hence (dA)/(dt) = 2 × 4 × 6 = 48 cm^{2}s^{-1}

## Each side of a square is increasing at a rate of 6 cm/s . At what rate is the area of the square increasing when the area of the square is 16 cm^{2} ?

**Summary:**

Each side of a square is increasing at a rate of 6 cm/s . At 48 cm^{2}s^{-1} rate, the area of the square is increasing when the area of the square is 16 cm^{2}.

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