The diagonals of a quadrilateral

thedarktiger · 2014-01-15 13:53:35

basicly I have all the lengths of a quad and I need to find the diagonal.
heres the problem:
The distance from Capital City to Little Village is 660 miles. From Capital City to Mytown is 310 miles, from Mytown to Yourtown is 200 miles, and from Yourtown to Little Village is 150 miles. How far is it from Mytown to Little Village?
no answer just please explain how to do this. You guys rock!

-the dark tiger

bobbym · 2014-01-15 15:02:46

Hi thedarktiger;

It is possible to find the distance you want but you seem to have a degenerate quadrilateral.
Could you check your distances again?

thedarktiger · 2014-01-15 16:37:22

nah thats the exact problem

bobbym · 2014-01-15 19:40:29

Hi;

Then I think that 3 of the towns all lie on a straight line.

Bob · 2014-01-15 20:45:37

hi thedarktiger,

I agree with bobbym.

I've given a hint for your triangle question, but that also leads to an odd result.

LATER EDIT:

No it doesn't. I've realised there's an upper bound as well as a lower bound. I've edited that post too.

Where are these questions from?

Bob

Last edited by Bob (2014-01-15 21:08:04)

thedarktiger · 2014-01-16 20:54:25

a math book AOPS geometry I am really bad at geometry

irspow · 2014-01-20 00:41:55

There is no way to answer that precisely, there simply is not enough information. Those distances are all magnitudes without any indication of direction. There was an assumption made by the textbook that was either missed by you or missed by them in editing. The distance can take on many values if you are not given any angles or direction. Again, these are magnitudes and not vectors. For any given assumption, you will get a different distance. If they all lie on a straight line the distance could be either 50 or 350 miles, depending on whether Yourtown lies beyond or before Littlevillage by 150 miles. If we try to assemble a quadrilateral, again, without the angles of sides in relation to each other it can take many forms. So you would be looking for a range of possible values and not a specific magnitude.

Bob · 2014-01-20 23:45:18

hi irspow

If these points were anywhere in (let's assume) 2D then you'd be right.

But, by an extension of the triangle inequality and noting that 310 + 200 + 150 = 660, there's only one interpretation, namely that these towns are in a straight line with Capital City and Little Village at the ends of that line.

Which is just as well, because the problem would not have a unique solution otherwise.

Bob

Math Is Fun Forum

#1 2014-01-15 13:53:35

The diagonals of a quadrilateral

#2 2014-01-15 15:02:46

Re: The diagonals of a quadrilateral

#3 2014-01-15 16:37:22

Re: The diagonals of a quadrilateral

#4 2014-01-15 19:40:29

Re: The diagonals of a quadrilateral

#5 2014-01-15 20:45:37

Re: The diagonals of a quadrilateral

#6 2014-01-16 20:54:25

Re: The diagonals of a quadrilateral

#7 2014-01-20 00:41:55

Re: The diagonals of a quadrilateral

#8 2014-01-20 23:45:18

Re: The diagonals of a quadrilateral

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