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- anonymous

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.

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- anonymous

- katieb

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- anonymous

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

- anonymous

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

Argh! Distributed wrongly.

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- anonymous

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

- anonymous

Or am I wrong about this?

- anonymous

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

A solution using Mathematica is attached.

- anonymous

I think I made a mistake.

- anonymous

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

- anonymous

Thanks very much!

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