July 28th, 2013, 01:18 AM  #1 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Similarity and possibly algebra oriented geometry question.
Hello, I would appreciate some help with the following question please. In the diagram, XP = 1/2 PQ, QY = 1/3 PQ and XR = 2/5 XZ. Find the ratio of the area of triangle QRZ to the area of triangle QYZ. The drawing is not drawn to scale. I have attached a picture of the diagram. Thanks for taking the time to respond! 
July 28th, 2013, 12:42 PM  #2 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Similarity and possibly algebra oriented geometry questi
Let , , and angle YXZ=. Then , , and . Area of triangle QRZ is and area of triangle . Let's express area of those triangles over m and n. Finally 
July 28th, 2013, 12:46 PM  #3 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Similarity and possibly algebra oriented geometry questi
Since I can't edit my post , I meant 
July 28th, 2013, 12:55 PM  #4  
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Similarity and possibly algebra oriented geometry questi Quote:
Really sorry for three posts in a row (if needed let admins deleted).  
July 28th, 2013, 03:00 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,241 Thanks: 1438 
It's simplest to post the entire corrected post, then ask a moderator to delete the inaccurate ones (if nobody has replied to them). Triangles with the same height have areas in proportion to the corresponding bases. Last edited by skipjack; April 30th, 2014 at 12:10 AM. 
July 28th, 2013, 04:03 PM  #6 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Similarity and possibly algebra oriented geometry questi
Okay, I'll keep that in mind.

July 28th, 2013, 10:33 PM  #7 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Re: Similarity and possibly algebra oriented geometry questi
Thanks for quick and detailed responses! It has helped clarify my problem. 
April 21st, 2014, 07:42 AM  #8 
Newbie Joined: Apr 2014 From: Indonesia Posts: 2 Thanks: 0  RE:Help
How to solve this problem without using trigonometry? How did skipjack arrived at his/her answer for the areas of the triangle? 
April 21st, 2014, 07:43 AM  #9 
Newbie Joined: Apr 2014 From: Indonesia Posts: 2 Thanks: 0 
How did you arrive at the areas of each triangle?

April 21st, 2014, 11:56 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,057 Thanks: 721 
It would be easier if you started your own thread, and ask your own question; hijacking an inactive thread (as you did) is a good way for your post to be missed... 

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In the diagram, XP=1/2PQ, QY=1/3PQ and XR=3/5XZ.,find the ratio of the area of QRZ to that of QYZ,in the figure ,XP= 1/2 PQ
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