## Ika_Kim 3 years ago somebody please help me..got test tonight but still dunn how to solve this... The base of a triangle increases at the rate 2cm per second, and height decreases at the rate of 1/2cm per second.Find the rate of change f its area when the base and height are of length 5cm... ? T.T helpp

1. Ika_Kim

anybody ??? :(

2. Ika_Kim

you know agent00smith ?

3. agent0smith

hmm.... we know $A = 0.5 b h$ $\frac{ db }{ dt } = 2 (cm/s)$ $\frac{ dh }{ dt }= -0.5 (cm/s)$ We need $\frac{ dA }{ dt } = ?$

4. Ika_Kim

chain rule ?

5. Ika_Kim

but we have t differentiate A with respect to ??

6. agent0smith

Yeah that's what i'm trying to think of...

7. Ika_Kim

o.O ok ... i really dunno how to relate that

8. zepdrix

Hmm are we assuming this is a right triangle? :o

9. zepdrix

I guess it would have to be, otherwise we need more information. :) Looks like agent was on the right track. Both $$\large b$$ and $$\large h$$ are variables. Just apply the product rule! :D

10. zepdrix

Differentiate with respect to time*

11. agent0smith

Yeah that's what I was thinking... differentiate A wrt t

12. Ika_Kim

huh ??? yeahh differentiate wrt time . that is wwhat we want to find

13. Ika_Kim

im not clear with that

14. agent0smith

But then that seems to make the actual values of the base and height unnecessary, but maybe that's okay.... $\frac{ dA }{ dt} = 0.5 \frac{ db }{ dt}\frac{ dh }{ dt}$

15. zepdrix

Woops, product rule! :O

16. zepdrix

$\large A=\frac{1}{2}bh$$\large A'=\frac{1}{2}b'h+\frac{1}{2}bh'$Something like that, yes? :D

17. Ika_Kim

huhh ????? how can...i dont undrstand...

18. Ika_Kim

urmmm let me try that

19. Ika_Kim

wow.....yeahh!!! correct answer !!! greatt !! thank you so much guys ! love uollsz!! :D

20. zepdrix

yay team \:D/

21. Ika_Kim

my mentors :)

22. agent0smith