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#1 2013-11-18 15:48:17

shivusuja
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Triangles

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

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

#2 2013-11-19 00:02:55

bob bundy
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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

Bob

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

#3 2013-11-19 00:40:27

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

#4 2013-11-19 15:12:55

shivusuja
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Re: Triangles

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

#5 2013-11-19 15:26:08

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

#6 2013-11-19 20:01:48

anonimnystefy
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Re: Triangles

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

Last edited by anonimnystefy (2013-11-19 20:02:10)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-11-21 00:03:07

Agnishom
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Re: Triangles

anonimnystefy wrote:

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

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'
'The whole person changes, why can't a habit?' -Alokananda