How Fast is the Area Changing in an Equilateral Triangle?

[Peppy]

I need help with the question: The heighth of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5cm?

 

[whozum]

The area of a triangle is A= 1/2*bh

You know dh/dt = 3cm/min


Try manipulating the above equations to an appropriate form where you can find the area as a function of height, and inhernetly its rate of change.

 

[HallsofIvy]

Write the equation, which whozum gave you, A= (1/2)bh, Use a relation between b and h that is true for all equilateral triangles (divide the triangle into two right triangles and use the Pythagorean theorem) to write A as a function of h only.
Finally, differentiate with respect to t to get a relation between dA/dt and dh/dt.