February 28th, 2014, 01:15 PM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  median
triangle abc have ac=3cm bc=4cm ad and ah are two Perpendicular medians of triangle find ab 
February 28th, 2014, 02:41 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: median Hello, mared! Please check the wording of the problem. Quote:
How can we have two medians from the same vertex? And what are "perpedicular medians"? [color=beige]. . [/color]Are they perpendicular to each other [color=beige]. . [/color]or perpendicular to the opposite side?  
March 1st, 2014, 12:10 AM  #3 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  Re: median
Triangle abc has ac = 3cm bc = 4cm ad and bh are two Perpendicular medians of triangle (perpendicular to each other). Find ab. 
March 1st, 2014, 05:47 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133  ?5 cm

March 3rd, 2014, 12:56 AM  #5 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  Re: median
Can you send the solution?

March 3rd, 2014, 10:07 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
The method was easy, albeit tedious. Apollonius's theorem provides equations relating the length of each median to the lengths of the sides of the triangle. As the medians are perpendicular, a third equation is obtainable by applying Pythagoras to the rightangled triangle with hypotenuse hd (which has half the length of ab) and having legs whose lengths are a third the lengths of the medians. One thus has three simultaneous linear equations in the squares of the lengths of the medians and of the side to be found.


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