An isosceles triangle has base B and height H. Assuming its area remains constant, express the rate of change of the base with respect to the height.

Question

An isosceles triangle has base B and height H.  Assuming its area remains constant, express the rate of change of the base with respect to the height.

anonymous · Answer

I'm getting -2A/h^2  Does that look right?

anonymous · Answer

My reasoning:

A= 1/2 b * h
2A = b * h 
b = 2A/h

db/dh 2A/h
 = db/dh 2A * h^-1 
= 2A * -h^-2
= -2A/h^2

anonymous · Answer

Argh!  Distributed wrongly.

anonymous · Answer

Right, but you don't differentiate Area...only height.

anonymous · Answer

Or am I wrong about this?

anonymous · Answer

Doesn't it mean that if we keep the Area constant, at what rate does the base change respective of the height?  That can't be 0, I wouldn't think.

anonymous · Answer

A solution using Mathematica is attached.

anonymous · Answer

I think I made a mistake.

anonymous · Answer

yes,  -2A/h^2 is the correct answer.

anonymous · Answer

Thanks very much!