wu :: forums
« wu :: forums - Problem with a square »

Welcome, Guest. Please Login or Register.
Feb 3rd, 2023, 2:25am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   putnam exam (pure math)
(Moderators: Eigenray, william wu, SMQ, Icarus, towr, Grimbal)
   Problem with a square
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Problem with a square  (Read 5590 times)
x2862
Newbie
*





   


Posts: 10
Problem with a square  
« on: Mar 24th, 2010, 2:48am »
Quote Quote Modify Modify

I'm pretty good at coordinate  geometry but this problem a friend gave me is stumping me. any ideas? Should I be using the law of cosines?
 
A square with a side of length x has a interior point of p. the location of point p is shuch that the distance to 3 corners of the square is 500, 300, and 400 feet measured in a clockwise direction.what is the length of the side of the square?
« Last Edit: Mar 24th, 2010, 3:03am by x2862 » IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Problem with a square   rect3312.png
« Reply #1 on: Mar 24th, 2010, 4:38am »
Quote Quote Modify Modify

You can solve it algebraically. There are two ways to put the three distances in the square (see attachment). Putting the origin at the left lower corner, you can pick an x-coordinate for P, and calculate the rest from there by solving
x = sqrt(32-a2) + sqrt(42-a2)  
x = a + sqrt(52-(32-a2))
 
or for the second case  
x = sqrt(42-b2) + sqrt(52-b2)  
x = b + sqrt(32-(42-b2))
 
It doesn't give particularly nice answers though.
« Last Edit: Mar 24th, 2010, 4:46am by towr » IP Logged


Wikipedia, Google, Mathworld, Integer sequence DB
Aryabhatta
Uberpuzzler
*****






   


Gender: male
Posts: 1321
Re: Problem with a square  
« Reply #2 on: Mar 24th, 2010, 10:20am »
Quote Quote Modify Modify

Perhaps this is useful: http://www.cut-the-knot.org/proofs/swivel.shtml
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Problem with a square  
« Reply #3 on: Mar 24th, 2010, 11:00am »
Quote Quote Modify Modify

I don't see any way to use that.
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Aryabhatta
Uberpuzzler
*****






   


Gender: male
Posts: 1321
Re: Problem with a square  
« Reply #4 on: Mar 24th, 2010, 5:57pm »
Quote Quote Modify Modify

on Mar 24th, 2010, 11:00am, towr wrote:
I don't see any way to use that.

 
Sorry about that, I posted that link without trying it myself. In any case, it is kind of related to the problem and some people might find it interesting.
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board