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Can a triangle be formed with these length constraints?

  1. Oct 28, 2016 #1
    1. The problem statement, all variables and given/known data
    There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio.
    Is this statement true or false...?
    2. Relevant equations
    $$Golden \space Ratio = \phi = 1.618... $$
    3. The attempt at a solution
    Actually I have no clue at all how to approach to this kind of question.
     
  2. jcsd
  3. Oct 28, 2016 #2

    Math_QED

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    When I give you 3 line segments with a random length, can you make a triangle with it?
     
  4. Oct 28, 2016 #3
    I guess so
     
  5. Oct 28, 2016 #4

    micromass

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    Take a paper, try to make a triangle with sides 1cm, 1cm and 10cm. Show us the triangle you found.
     
  6. Oct 28, 2016 #5
    Actually there is a theorem called triangle inequality theorem, which states given ABC triangle, which has a,b,c length sides a+b>c , a+c>b and b+c>a must be true. therefore no need to show it to you that I cant create a triangle out of those sides 1,1 and 10.
     
  7. Oct 28, 2016 #6
    Actually this gives me an idea how to approach the question.
    i can try to get a result for r by solving three inequalities
    $$3r^2 +3 > 3r$$ $$3r^2+3r>3$$ $$3+3r>3r^2$$
     
  8. Oct 28, 2016 #7
    Eventually one inequality leads that r has a complex variance. (by solving 3r^2 +3 > 3r)
     
  9. Oct 28, 2016 #8

    micromass

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    Is,'t that trvially satisfied?
     
  10. Oct 28, 2016 #9
    I don't get what you say here.
     
  11. Oct 28, 2016 #10
    But in a sense I can say that r is not strictly a real number hence the statement is false... Am I right???
     
  12. Oct 28, 2016 #11
    No I was wrong all along... I solved it. The statement is true. All r is real and greater than Golden Ratio (1.61803)...
     
  13. Oct 28, 2016 #12

    fresh_42

    Staff: Mentor

    So ##r=10## is obviously greater than ##\phi## and you've found a triangle with sides ##3, 30## and ##300##?
    Which curvature do you assume your geometry has?
     
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