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

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

THANKS

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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

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

*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

The knowledge of some things as a function of age is a delta function.

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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