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October 3rd, 2012, 04:15 PM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002  Right triangle area
Right triangle ABC, the 2 legs being a and b. Let radius of incircle = r Show that area of ABC = (a  r)(b  r) Kinda fun! 
October 3rd, 2012, 06:08 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond  Re: Right triangle area 
October 3rd, 2012, 07:07 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Right triangle area
[attachment=0:14dz3n3u]Denistriangle.jpg[/attachment:14dz3n3u] By Pythagoras: 
October 3rd, 2012, 07:09 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002  Re: Right triangle area
Nice one Greg. I went this way: (a  r) (b  r) = area? Since r = (a + b  c) / 2 : [a  (a + b  c) / 2] * [b  (a + b  c) / 2] = area Expand and simplify: (c^2  a^2  b^2 + 2ab) / 4 = area Since c^2  a^2  b^2 = 0, then: 2ab / 4 = area ab / 2 = area Anything "wrong"? Doesn't "feel" 100% ok ! 
October 4th, 2012, 02:19 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
Nothing is wrong, but there is no need to repeat "= area" until the end. (a  r)(b  r) = (a  (a + b  c)/2)(b  (a + b  c)/2) = (c + a  b)(c  a + b)/4 = (c²  (a  b)²)/4 = (c²  (a² + b²) + 2ab)/4 = ab/2 = area of triangle ABC. 
October 4th, 2012, 03:40 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002  Re: Right triangle area
OOOOOOOOOOOOOOOOOOOKKKKKKKKKKKKKKKKKKKKKKK! Thanks, Skip.


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