Related Rates Help

[suicoted]

8. The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 10 cm^2?

Please show how you solved it with calculus. Thx.

 

[pka]

The area as a function of time is: A(t)=(0.5)b(t)h(t).
Where b(t) is the base as function of time, h(t) is the height.
A’(t)=(0.5)[b’(t)h(t)+b(t)h’(t)], thus 2 = (.05)[b’(t)(10)+b(t)(10)].
To finish this problem we need to solve for b’(t),
To do that you also need to find b(t), the base when A=10 and h=10.

 

[suicoted]

Thx

Thanks pka. I used your method to figure out the answer, and it matches the solutions at the back. I forgot to use the product rule when doing the derivative, thx. [/b]