Homework Help: Circumference of a parallelogram (diagnoals given only)

1. Feb 15, 2008

ViresArcanum

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. Feb 15, 2008

sutupidmath

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
3. Feb 16, 2008

ViresArcanum

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...

4. Feb 18, 2008

Jamil (2nd)

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