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 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:
 $\text{Triangle }abc\text{ with }ac= 3\text{ cm},\,bc = 4\text{ cm}$ $ad\text{ and }ah\text{ are two perpendicular medians of triangle.}$[color=beige] /[/color][color=red]??[/color] $\text{Find }ab.$

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: 20,966 Thanks: 2216 ?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: 20,966 Thanks: 2216 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 right-angled 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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