Math Help - related rates

1. related rates

A triangle is increasing in size. The base is increasing at a rate of 5 ft/s while the height is increasing at a rate of 2 ft/s. At what rate is the area increasing at the instant the base of the triangle is 10 ft and the height is 6 ft?

hurts my brain

2. Originally Posted by xSMUxCHEERLEADINGx
A triangle is increasing in size. The base is increasing at a rate of 5 ft/s while the height is increasing at a rate of 2 ft/s. At what rate is the area increasing at the instant the base of the triangle is 10 ft and the height is 6 ft?

hurts my brain
Area of triangle is:

$A(t)=\frac{b(t)h(t)}{2}$

where $b(t)$ and $h(t)$ are the base and height at time $t$.

So (using the product rule):

$A'(t)=\frac{b(t)h'(t)+b'(t)h(t)}{2}$

Now you want to find $A'(t)$ when $b'(t)=5$ ft/s , $h'(t)=2$ ft/s, $b(t)=10$ ft, $h(t)=6$ ft

CB

3. I got 25 ft per second