# Thread: related rates

1. ## related rates

I keep getting stuck, any help is much appreciated!

Question:

A rectangle initially has the dimensions 2cm by 4cm. All sides begin increasing in length at a rate of 1cm/s. At what rate is the area of the rectangle increasing after 20 s.

2. ## Re: related rates

The length will be $\displaystyle (4+t)$cm. The width will be $\displaystyle (2+t)$cm. What will the area be? Find something of the form $\displaystyle A=f(t)$ and differentiate this to get something of the form $\displaystyle \frac{dA}{dt}=f'(t)$.

3. ## Re: related rates

so area would be (4+t)(2+t) and after multiplying that I get t^2+6t+8. When I differentiate, that gives me the rate, correct? Which would be 2t+6 and when t=20s, the rate would be 46cm/s?

4. ## Re: related rates

Looks good. When $\displaystyle t=19$, the area is $\displaystyle (21)(23)=483$, and when $\displaystyle t=20$, the area is $\displaystyle (22)(24)=528$, an increase of $\displaystyle 45$, and when $\displaystyle t=21$, the area is $\displaystyle (23)(25)=575$, an increase of $\displaystyle 47$, which suggests that when $\displaystyle t=20$, the rate of increase is $\displaystyle 46$cm/s.

5. ## Re: related rates

Awesome! Thank you so much!