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Circumference of a parallelogram (diagnoals given only)

  1. Feb 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Given is a parallelogram which has diagonals of the length 7 (e) and 9 units (f). How big is its circumference?

    The sides are a,b,c,d; a being the bottom side, rest is anti-clockwise... alpha is the angle of a etc...


    2. Relevant equations

    no are given, i guess pythagoras or trig might be useful.

    diagonals of a parallelogram (might be useful)

    e=sqrt(a^2+d^2+2*a*d*cos(alpha))
    f=sqrt (a^2+d^2-2*a*d*cos(alpha))

    alpha=gamma
    beta=delta
    beta=180-alpha

    3. The attempt at a solution

    I tried using this first of all by drawing lots of triangles in the parallelogram and solve it with pythagoras or trig functions but without success

    afterwards i tried using the formulas for the diagonals but without knowing a and d i didn't have much of a success either
     
  2. jcsd
  3. Feb 15, 2008 #2
    is it a regular parallelogram, where a=d, b=c, or not regular one where all, a,b,c,d are of different value?
    I am a little bit confused, are these
    alpha=gamma
    beta=delta
    beta=180-alpha some other conditions that you are given, or what?
     
    Last edited: Feb 15, 2008
  4. Feb 16, 2008 #3
    well, a=c and b=d

    since the opposing sides are equally long, the opposing angles have to be equal as well; since a=c, alpha=gamma

    these angle conditions are just normal rules for a regular parallelogram

    hope, this is less confusing now...
     
  5. Feb 18, 2008 #4
    I am giving a hint:

    The diagonals of a parallelogram always intersect in the middle.

    EDIT: Talking of midpoints, the question does not hold enough information. If you rotate any of the diagonals from the mid-point, the circumference (or is it the perimeter?) will vary. Thus the question is not finite.
     
    Last edited: Feb 18, 2008
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