A metal plate in the shape of an equilateral triangle is being heated in such a way that each of the sides is increasing at the rate of ten inches per hour. How rapidly is the area increasing at the instant when each side is 69.28 inches?
$$A_{et} = \frac{\sqrt{3}}{4}s^2.$$
So, $$\frac{dA_{et}}{dt} = \frac{\sqrt{3}}{2}s\frac{ds}{dt} = \frac{\sqrt{3}}{2}(69.28 in)(10 \frac{in}{hr}) = 599.982399742 \frac{in^2}{hr} \approx 600 \frac{in^2}{hr}$$
In minutes,
$$600 \frac{in^2}{hr} * \frac{1 hr}{60 min} = 10 \frac{in^2}{min}.$$
The book's answer: $60 \frac{in^2}{min}$