Question

the side of a square is increasing at a rate of 5cm/s. at what rate is the perimeter changing?

Answer 1

This is a related rates problem, or something like that. If we draw a square and label its sides 's' like this:Since the Perimeter is a function of the side length which is a function of time, we use Chain Rule to differentiate to find dP/dt: \[\bf P = 4s, \ \frac{ ds }{ dt }=5 \ cm/s\]Differentiating both sides of the Perimeter equation gives us:\[\bf \frac{ dP }{ dt }=4\frac{ ds }{ dt }=4(5 \ cm/s)=20 \ cm/s\]

Answer 2

thank you