June 6th, 2012, 06:15 AM  #1 
Member Joined: Jan 2012 Posts: 72 Thanks: 0  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.

June 6th, 2012, 07:35 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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: 
June 6th, 2012, 08:23 PM  #3 
Member Joined: Jan 2012 Posts: 72 Thanks: 0  Re: Rate of change
thanks


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