Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#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
Offline
#2 2013-11-18 01:02:55
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,621
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
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#3 2013-11-18 01:40:27
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'
I'm not crazy, my mother had me tested.
Offline
#4 2013-11-18 16:12:55
- shivusuja
- Member
- Registered: 2006-09-14
- Posts: 56
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?
Offline
#5 2013-11-18 16:26:08
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'
I'm not crazy, my mother had me tested.
Offline
#6 2013-11-18 21:01:48
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Triangles
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.
Offline
#7 2013-11-20 01:03:07
Re: Triangles
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'
I'm not crazy, my mother had me tested.
Offline