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#1 2013-05-28 11:03:21

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

triangle inequality

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
lol

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#2 2013-05-28 12:39:38

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

Re: triangle inequality

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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#3 2013-05-28 13:42:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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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#4 2013-05-28 14:18:12

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

Re: triangle inequality

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
lol

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#5 2013-05-28 16:58:21

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

Re: triangle inequality

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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#6 2013-05-28 17:29:46

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

Re: triangle inequality

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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#7 2013-05-28 21:34:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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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#8 2013-05-29 00:39:02

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

Re: triangle inequality

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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#9 2013-05-29 12:17:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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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#10 2013-05-30 02:19:52

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

Re: triangle inequality

Hello bobbym;

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

I could not get this one. sad

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#11 2013-05-30 02:21:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

Hi;

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


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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#12 2013-05-30 02:22:58

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

Re: triangle inequality

Doesn't that number appear to be too large?

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#13 2013-05-30 02:25:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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?


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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#14 2013-05-30 02:27:50

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

Re: triangle inequality

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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#15 2013-05-30 02:29:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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


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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#16 2013-05-30 02:32:34

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

Re: triangle inequality

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

Where are we going for your birthday?

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#17 2013-05-30 02:35:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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.


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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#18 2013-05-30 02:38:24

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

Re: triangle inequality

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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#19 2013-05-30 02:40:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

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...


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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#20 2013-05-30 02:49:10

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

Re: triangle inequality

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

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#21 2013-05-30 02:50:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

Oh boy! I never could turn that down.


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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#22 2013-05-30 02:54:18

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

Re: triangle inequality

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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#23 2013-05-30 03:04:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality

Hi;


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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#24 2013-05-30 03:09:43

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

Re: triangle inequality

Hi


“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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#25 2013-05-30 03:19:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: triangle inequality


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.

Offline

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