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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

Two sides of an obtuse triangle are 16 and 21. How many possible lengths are there for the third side, if it is a positive integer?

I see you have graph paper.

You must be plotting something

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**{7/3}****Member**- Registered: 2013-02-11
- Posts: 210

In a triangle,a side must be smaller than the sum of other two sides,so the third side will be smaller than 16+21=37,which means there are 36 possible lengths.

There are 10 kinds of people in the world,people who understand binary and people who don't.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Hi;

It has to be less than that, sides 1,2,3,4,5 are not possible. Taking into account that the triangle must be obtuse may make that even less.

**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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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

yea, I used several equations

EDIT: i got it

Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer?

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Lengths 6 to 13 work for the first problem. There are 8 solutions.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**{7/3}****Member**- Registered: 2013-02-11
- Posts: 210

Sorry,i mistook.by the way why won't 27 to 36 work for the first problem

There are 10 kinds of people in the world,people who understand binary and people who don't.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

I am getting 18 solutions for the first problem.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Ah, yes, 27 to 36 also work. 18 solutions it is.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Hi;

cooljackie wrote:

Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer?

**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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Hello bobbym;

I need to see your solution and how you know it is right.:)

I could not get this one.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Hi;

I am not at all sure on this one. It required some research and some M to get the job done.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Doesn't that number appear to be too large?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Hi;

Doesn't that number appear to be too large?

Not really, that can verified. What I do not get is why I am having so much trouble drawing it in geogebra. Did you have more luck there?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Your brother tried to help me with it while you were sleeping. I do not handle geogebra that well. How do you know that answer is okay?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Calculations are proving the triangle is feasible but until I can illustrate it, I have no faith in the answer...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

I got that answer now too! Your brother is a great mathematician.

Where are we going for your birthday?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

He is really good at differential geometry. He is more physics oriented than I am too.

Where are we going for your birthday?

Any place where you are paying. I am not particular.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Any place where you are paying. I am not particular.

How wonderful of you but I can do that.

Please post all the results when you get them.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

I will probably post them in Computer math once I have a working geogebra solution to it.

How wonderful of you

Cmon, you are embarassing me.

I had planned on playing some pool on that day or maybe some bball against the local toughs. Something physical...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

You should just take it easy and relax. We can watch a Cameron Diaz movie. Your choice

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Oh boy! I never could turn that down.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi bobbym

Try the triangle with

*Last edited by anonimnystefy (2013-05-30 03:01:42)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,478

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**