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#1 2013-11-17 16:48:17

shivusuja
Member
Registered: 2006-09-14
Posts: 56

Triangles

Please Help Me Out

Sum Of The Altitudes Of Triangle Is Less Than He The Sum Of The Sides Of The Triangle.
(ae+cf+bd < Ab+bc+cd)


Proof
I Have Tried With
Sum Of The Two Sides Is Greater Than The Third Side
Abc As Sides Of The Triangle And Ae. Bd And Cf As The Altitude.
I Got

Ae+ec>ac      Bd+dc>bc   Cf+af>ac
Ae+be>ab      Bd+ad>ab   Cf+fb>bc

Adding All I Got 2ae+2bd+2cf>ab+bc+ca

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#2 2013-11-18 01:02:55

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Triangles

hi shivusuja

I spent ages working around the triangle inequality and got nowhere.  Then I had a fresh idea.

AEC is a right angled triangle with AC as hypotenuse.  So

AE < AC

Similarly, in triangle CFB

CF < BC

And finally, in triangle ABD

BD < AB

Add those up and

AE + CF + BD < AC + BC + AB

smile

Bob


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

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#3 2013-11-18 01:40:27

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,968
Website

Re: Triangles

Thank You, Bob


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2013-11-18 16:12:55

shivusuja
Member
Registered: 2006-09-14
Posts: 56

Re: Triangles

THANKS roflol
SO SIMPLE WHOLE DAY I WORKED OUT. THIS IS 5 MARKS QUESTION. DO I GET 5 MARKS IF I DO IN THIS WAY?

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#5 2013-11-18 16:26:08

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,968
Website

Re: Triangles

Yes, atleast in CBSE


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2013-11-18 21:01:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,602

Re: Triangles

The harder question is, can you prove the same thing, but with medians instead of heights? smile

Last edited by anonimnystefy (2013-11-18 21:02:10)


“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 2013-11-20 01:03:07

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,968
Website

Re: Triangles

anonimnystefy wrote:

The harder question is, can you prove the same thing, but with medians instead of heights? smile

A similar question came in my test and I could not answer


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

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