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wu :: forums    riddles    easy (Moderators: Eigenray, Icarus, SMQ, Grimbal, ThudnBlunder, william wu, towr)    Triangles « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Triangles  (Read 873 times) codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 Triangles   Untitled2.png « on: Mar 3rd, 2009, 11:34am » Quote Modify 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  ) IP Logged You miss 100% of the shots you never take. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Triangles   « Reply #1 on: Mar 3rd, 2009, 12:45pm » Quote Modify 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. « Last Edit: Mar 3rd, 2009, 12:59pm by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Triangles   « Reply #2 on: Mar 3rd, 2009, 12:53pm » Quote Modify on Mar 3rd, 2009, 12:45pm, towr wrote: 1/4th [...] QR is half of AC Come again?!   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. --SMQ IP Logged --SMQ towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Triangles   « Reply #3 on: Mar 3rd, 2009, 12:59pm » Quote Modify on Mar 3rd, 2009, 12:53pm, 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]   « Last Edit: Mar 3rd, 2009, 1:01pm by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 Re: Triangles   « Reply #4 on: Mar 3rd, 2009, 5:56pm » Quote Modify Yes SMQ. hahaha towr. IP Logged You miss 100% of the shots you never take. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Triangles   triangle18.GIF « Reply #5 on: Mar 4th, 2009, 5:41am » Quote Modify I count 18. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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