Groll!

Geometry Level 3

In a triangle A B C ABC , the sides are of length 16 , 18 , 20 16,18,20 respectively. The medians drawn to them are of lengths approximately 13.78 , 17.26 , x 13.78,17.26,x respectively.

Find x x correct upto two decimal places.


The answer is 15.72.

Krishna Ar by Krishna Ar , 21, India

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2 solutions

http://s29.postimg.org/gbhaxdnmf/triangles.png http://s29.postimg.org/gbhaxdnmf/triangles.png

Large Version: Here

Now, what is Groll?

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Cool diagram; is that Geogebra?

We could also use Appolonius' theorem: link

Brian Charlesworth - 6 years, 9 months ago

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yep, that is Geo. Thanks for the link

Agnishom Chattopadhyay - 6 years, 9 months ago

Geo+Troll! :P

Krishna Ar - 6 years, 9 months ago

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Oh. I thought you were yelling in German. Guess not. :)

Brian Charlesworth - 6 years, 9 months ago

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Yeah! Groll is German for angry tirades. D'ya know German too? :)

Krishna Ar - 6 years, 9 months ago

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@Krishna Ar – Haha. No, but my niece is fluent in 5 languages so I asked her if she knew what it meant. I think, however, that the "geo+troll" interpretation is more relevant to the question at hand. :)

Brian Charlesworth - 6 years, 9 months ago

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@Brian Charlesworth – :D. How nice! ^_^

Krishna Ar - 6 years, 9 months ago
Girija Lenka
Feb 20, 2015

16^{2} +20^{2}=2[AD^{2}+9^{2} solving this equation we get ad as 15.716..

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