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February 28th, 2014, 01:15 PM   #1
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median

triangle abc
have ac=3cm
bc=4cm
ad and ah are two Perpendicular medians of triangle
find ab
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February 28th, 2014, 02:41 PM   #2
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Re: median

Hello, mared!

Please check the wording of the problem.


Quote:


[color=beige] /[/color][color=red]??[/color]


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?

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March 1st, 2014, 12:10 AM   #3
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Re: median

Triangle abc
has ac = 3cm
bc = 4cm
ad and bh are two Perpendicular medians of triangle
(perpendicular to each other).
Find ab.
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March 1st, 2014, 05:47 PM   #4
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?5 cm
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March 3rd, 2014, 12:56 AM   #5
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Re: median

Can you send the solution?
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March 3rd, 2014, 10:07 AM   #6
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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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