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## #1 2012-10-10 23:35:52

tyteen4a03
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### How to tell impossible length combination of triangle

I just answered this question but was unable to come up with some kind of formula to tell the user that some combinations of a triangle is impossible. Is there any kind of formula to tell if a combination of a triangle is impossible?

## #2 2012-10-10 23:39:22

bobbym

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### Re: How to tell impossible length combination of triangle

Hi;

That link does not show the problem, so I deleted it to prevent confusion.  Please copy the problem here. Then it can be answered.

I think I can deduce what you are asking.

For any combination of three lengths a,b,c this must be true to form a triangle.

a+b>c
b+c>a
a+c>b

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2012-10-10 23:49:19

tyteen4a03
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### Re: How to tell impossible length combination of triangle

Oh, sorry. The problem is:

Three towns are arranged in the shape of a triangle. The distance from Stockton to Overly is 10 miles and the distance from Overly to Shea is 8 miles. Maria drives from Stockton to Overly to Shea and back to Stockton. Which of the following statements best describes her trip?

i.imgur.com/6UUsh.png

She drove 19 miles.
She drove 36 miles.
She drove less than 36 miles.
She drove more than 36 miles.

Last edited by tyteen4a03 (2012-10-10 23:49:29)

## #4 2012-10-10 23:56:02

bobbym

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### Re: How to tell impossible length combination of triangle

The answer is, she drove less than 36 miles.

Simple consequence of

a+b>c
b+c>a
a+c>b

when a,b,c are the sides of any triangle.

Call Shea to Stockton d and then you know that d < 10 + 8. Therefore only answer c is possible.

You are a programmer?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #5 2012-10-11 00:00:28

bob bundy
Moderator

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### Re: How to tell impossible length combination of triangle

hi tyteen4a03

Welcome to the forum.

I've made a diagram.  Click below.

You may start by fixing Stockton and Overly at 10 miles apart.

But you don't know exactly where Shea is, in relation to these two.

So I've drawn a circle, radius 8 miles.  Shea must lie somewhere on this circle, so you can consider the possibilities by thinking about the nearest it could be and so on.

Hope that helps,

Bob