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June 6th, 2012, 06:15 AM   #1
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Rate of change

An isosceles triangle has fixed base of length b cm. The other 2 equal sides of the triangle are each decreasing at the constant rate of 3cm per second. How fast is the area changing when the triangle is equilateral? Leave your answer in terms of b.
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June 6th, 2012, 07:35 AM   #2
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Re: Rate of change

Let s be the equal sides of the isosceles triangle and h be the height. We then have the area A is:



By Pythagoras, we have:



Hence:



Implicitly differentiate with respect to time t:



We are given thus:



Now, when we have:

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June 6th, 2012, 08:23 PM   #3
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Re: Rate of change

thanks
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