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# parallelogram

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31 May 2009, 05:54
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One of the inside angles of a parallelogram is 60 degree. What is the ratio of the length of two diagonals?
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Joined: 08 Feb 2009
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31 May 2009, 07:00
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IMO the ratio of the diagonals is 1:$$\sqrt{3}$$

Opposite angles of the parallelogram are equal.

Draw the diagonals. Diagonals are angle bisectors in paralleogram.

Once the two diagonals are drawn, it would result in 4 triangles inside the parallelogram.

Each of those triangles is a 30-60-90 triangle $$\Rightarrow$$ The sides of that triangle are in the ratio 1:$$\sqrt{3}$$.

Add the ratios together $$\Rightarrow$$ the diagonals are in the ratio 2:2$$\sqrt{3}$$ $$\Rightarrow$$ 1:$$\sqrt{3}$$.
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31 May 2009, 15:51
diagonals of the 60-120 parallelogram form 30-60-90 triangles.
The sides are in the ratio 1/(sqrt)3.
So , the diagonals are also in the ratio 1/(sqrt)3.
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Lahoosaher

Re: parallelogram   [#permalink] 31 May 2009, 15:51
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