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Parallelogram Park


spoud74

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There is a park in a parallelogram shape. Person A walks along the longer diagonal. Person B walks along the shorter one. Does A cover 1.5 times the distance B covers?

1. Parallelogram has one side 1 km and another side 2km

2. One of the internal angles of the parallelogram is 60 degrees

 

Question is essentially asking if one diagonal is 1.5 times the other diagonal.

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  • 1 year later...

Have a doubt regarding the second condition:

 

We know that the relative size of side corresponds to the angle opposite it.

i.e. The greater the angle the greater the side opposite it.

 

In this problem we know that one angle is 60 and the other is 120. i.e double the other.

 

As the sides subtending these angles is the same(1 and 2 in this case), can we relate that the side opposite 120 is double that opposite 60?

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  • 1 month later...
(1) Inufficient. The diagonals will be such that 1

(2) Angles are known, but not the sides.

 

Combining: sufficient, since for given angles & sides, the diagonals are fixed, whatever their values are.

 

C

Makumajon, how do you know that the diagonal is 1

Secondly, how can knowing the angles and the sides help in solving this.

Assuming this to be a PS question, can you show how to solve. Thanks

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Simply apply the parallelogram theorem of vector addition. If you are not aware of this theorem, which might be the case if you are not a science student, please let me know. I would try another way.

Sorry, I do not know this theorem ... please help to solve in some other way ... Thanks

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True for a square and rhombus, not for typical parallelogram or rectangle. First draw a parallelogram. Then extend the larger side keeping other things constant; you would see that the larger diagonal is moving to the larger side, becoming closer to it, thus reducing one angle but increasing the other angle.
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