The question is:

The height h of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5 cm? Give the answer to 2 decimal places.

How can I figure this question out?

Thank You!

- March 7th 2009, 07:38 PMMeeklo BracaCould I get some help finding how fast a triangle's area is changing?
The question is:

The height h of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5 cm? Give the answer to 2 decimal places.

How can I figure this question out?

Thank You! - March 8th 2009, 12:52 AMearboth
1. The area of a triangle is calculated by

2. In an equilateral triangle the sides are equal and the height is calculated by:

3. Plug in this term instaed of s into the equation of the area:

4. Calculate the first derivation of a to get the speed of change:

Now calculate a'(5):

- March 9th 2009, 05:37 PMMeeklo Braca
Isnt the derivative equation

da/dt=(1/3)sqrt3h * dh/dt

Isnt your equation missing the dh/dt with a final answer being 8.66? - March 9th 2009, 09:44 PMmr fantastic