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**tyteen4a03****Member**- Registered: 2012-10-10
- Posts: 2

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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**tyteen4a03****Member**- Registered: 2012-10-10
- Posts: 2

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

The answers are:

She drove 19 miles.

She drove 36 miles.

She drove less than 36 miles.

She drove more than 36 miles.

Thanks for answering.

*Last edited by tyteen4a03 (2012-10-10 00:49:29)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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