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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: 6,421

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: 17,134
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 made a human being happy! There is no further achievement.' -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: 17,134
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 made a human being happy! There is no further achievement.' -bobbym

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 17,134
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 made a human being happy! There is no further achievement.' -bobbym

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