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 April 22nd, 2011, 12:32 PM #1 Member   Joined: Feb 2009 Posts: 54 Thanks: 0 Change of triangle height Height if triangle is 32 while width is 24. The area doesn't change but the height is changing 3 meters per sec. Find out how fast does width change. I tried to do it but still don't understand the unit/time concept. Also I don't understand what is $\frac{dV}{dt}$
 April 22nd, 2011, 12:43 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: Change of triangle height We have: $A=\frac{1}{2}bh$ Differentiating with respect to time, noting A is a constant, we have:  $b\frac{dh}{dt}+\frac{db}{dt}h=0$ $\frac{db}{dt}=-\frac{b}{h}\frac{dh}{dt}$ We see that the base b (width) changes in the opposite direction of the height. With the values given, we find: $\frac{db}{dt}=-\frac{24}{32}$$3\text{ \frac{m}{s}}$$=-\frac{9}{4}\:\text{ \frac{m}{s}}$

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### sum of distances in equilateral triangle equals to height

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