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        riddles >> easy >> Triangles
        
(Message started by: codpro880 on Mar 3^rd, 2009, 11:34am)

Title: Triangles
Post by codpro880 on Mar 3^rd, 2009, 11:34am

Equilateral triangle ABC has altitudes BX and AY that intersect at point P. QR, containing point P, is parallel to AC. What fraction of the area of triangle ABC is the triangle PYR?
Explain thoroughly.

(I realize I don't have R labeled :-/)

Title: Re: Triangles
Post by towr on Mar 3^rd, 2009, 12:45pm

[hide]1/4th
Because P is the center of the equilateral triangle, and so QR is half of AC and QR=QX=XR, which divide the triangle in 4 equal pieces.[/hide]

Title: Re: Triangles
Post by SMQ on Mar 3^rd, 2009, 12:53pm

on 03/03/09 at 12:45:56, towr wrote:

[hide]1/4th [...] QR is half of AC[/hide]

Come again?! ;)

[hide]P is indeed the center of the equilateral triangle, but QR = (2/3)AC, so PR = AC/3. Moreover, since angle PYR is right, triangle PYR is 30-60-90 with hypotenuse AC/3, and thus half of an equilateral triangle with side AC/3. Such a triangle would have area 1/9 ABC, so triangle PYR has 1/18 the area of ABC.
[/hide]
--SMQ

Title: Re: Triangles
Post by towr on Mar 3^rd, 2009, 12:59pm

on 03/03/09 at 12:53:13, SMQ wrote:

Come again?! ;)

Yeah, sorry. I shouldn't be answering puzzles during the opening credits of anime..
[edit]Let alone answering something that isn't even the question[/edit]

Title: Re: Triangles
Post by codpro880 on Mar 3^rd, 2009, 5:56pm

Yes SMQ.
hahaha towr.

Title: Re: Triangles
Post by Grimbal on Mar 4^th, 2009, 5:41am

I count [hide]18[/hide].