## ashleynguyenx3 3 years ago The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

1. asnaseer

start by assigning a variable to represent the side length of the square. lets call it x. now, what would be the area of the square in terms of x?

2. ashleynguyenx3

100?

3. asnaseer

no - what is the area of a square if its side length is equal to x?

4. ashleynguyenx3

I don't get it

5. asnaseer

|dw:1350248149705:dw|

6. ashleynguyenx3

Oh, A=x^2

7. asnaseer

:)

8. asnaseer

good, so now you just need to differentiate both sides with respect to time (t). Do you know how to do that?

9. ashleynguyenx3

Derivative, right?

10. asnaseer

yes

11. ashleynguyenx3

dA/dt=2x(dx/dt)

12. asnaseer

perfect! almost there now...

13. asnaseer

now, when the area is 150 cm^2, then what would the side length of the square equal?

14. asnaseer

i.e. what is the length of the side of a square if its area is 150 cm^2?

15. ashleynguyenx3

sq rt of 150?

16. asnaseer

yes

17. ashleynguyenx3

So you would plug in x and dx/dt to get dA/dt?

18. asnaseer

now, in the equation you derived, you got:$\frac{dA}{dt}=2x\frac{dx}{dt}$Your questions tells you how fast the side length is increasing, so this gives you the value for:$\frac{dx}{dt}=10$

19. asnaseer

yes - you have it now - well done! :)

20. ashleynguyenx3

Yay, thank you! :)

21. asnaseer

yw :)

22. ashleynguyenx3

I would ask for more help, but it's okay.

23. asnaseer

?

24. ashleynguyenx3

I don't really understand related rates.

25. asnaseer

What you should do is find a specific example and then post that as a question. Otherwise it becomes difficult to explain in general terms.

26. asnaseer

For example, in this question, the rate of increase of side length is RELATED to the rate of increase of area by the formula you just derived.

27. ashleynguyenx3

Well, I'm just doing this packet. I understand some, but not all. http://tutorial.math.lamar.edu/ProblemsNS/CalcI/RelatedRates.aspx

28. asnaseer

In that case I would advise you to pick one that you don't understand and post it as a question. If you also include what parts of it you DO understand then it becomes easier for others to focus on the parts that you are having difficulties with.

29. ashleynguyenx3

Okay, thanks again :D