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A tricky geometry problem! Please help

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data

    In Rectangle ABCD, AB=4 and BC=3. Find the side length of Rhombus AXYZ, where X is on AB, Y is on BC and Z is on BD.

    2. Relevant Questions:


    3. The attempt at a solution

    Hi, so here's my picture for the problem...I tried to draw the exact picture with exact value of the problem (using rulers, compass, etc.)
    https://mail.google.com/mail/u/0/?ui=2&ik=65096f80a0&view=fimg&th=142e05c217ab4a7e&attid=0.1&disp=inline&safe=1&attbid=ANGjdJ8VlUlSyOcZxwQH7UU8SWsWZZS5AQMIGuuyqaGtZEzxSajqjBH3pw_2NeEwrZCyqh-ea_Lq9g6IEgwbZ80bNLtI2nwqrzmgJlmwZALZiJEnTpNHIJZJno8zncw&ats=1386743610684&rm=142e05c217ab4a7e&zw&sz=w1488-h627
    I was able to find a pair of similar triangles and figured out that: YZ = (4/3)BY
    I didn't get really far after that...
    Please help me !!!
     
  2. jcsd
  3. Dec 11, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    YZ = (4/3)BY is correct. Use the other property of the rhombus, that all sides are of equal length.


    ehild
     
  4. Jan 29, 2017 #3
    40700d803214069171fe87bec1811471c283e285.png is a rhombus implies d1dd0ff0c99be4bb0ed589e9fea29bb8f4a5ecb4.png . In 1a7a0327109ede54bf3abf9eb325bb58a503afc2.png by similarity we get 6d282a64f3a730b4fadbba8d53d29a28e9003bcd.png

    And then we get 081b45483abfce53e98405dcacc80c9801fec8f0.png . Thus, we result in the equation a0ccde74f902f48e407c67b4dd90cf551630994d.png .

    Sorry if the LaTeX or images I put in my reply don't come out properly

    ET ag
     
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