The sides of a square increase in length


The sides of a square increase in length at a rate of 2 m/s.

a) At what rate is the area of the square changing when the sides
are 10 m long?

b) At what rate is the area of the square changing when the sides
are 20 m long?

Solution

Let A represent area and x represent the side length of the square.

A = x^{2} (take the derivative with respect to time, use chain rule)

A^\prime=2x\cdot x^\prime(t) (A^\prime now represents the rate of change for area)

a) When the sides are 10m long:

A^\prime= 2(10m)\cdot(2\frac{m}{s}) = 40\frac{m^2}{s}

b) When the sides are 20m long:

A^\prime = 2(20m)\cdot(2\frac{m}{s}) = 80\frac{m^2}{s}

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