Math Goodies is a free math help portal for students, teachers, and parents.
|
Interactive Math Goodies Software

testing left nav
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums  Parent Forum  Parent's Place  TRIANGLES New Topic  Reply to Topic  Printer Friendly
Author  Topic

sreesuja
Average Member

India
13 Posts

 Posted - 11/17/2013 :  23:46:14 PLEASE HELP ME OUTSUM OF THE ALTITUDES OF TRIANGLE IS LESS THAN HE THE SUM OF THE SIDES OF THE TRIANGLE.(AE+CF+BD < AB+BC+CD)PROOFI HAVE TRIED WITHSUM OF THE TWO SIDES IS GREATER THAN THE THIRD SIDEABC AS SIDES OF THE TRIANGLE AND AE. BD AND CF AS THE ALTITUDE.I GOTAE+EC>AC : BD+DC>BC : CF+AF>ACAE+BE>AB : BD+AD>AB : CF+FB>BCADDING ALL I GOT 2AE+2BD+2CF>AB+BC+CA

the_hill1962

USA
1468 Posts

 Posted - 11/18/2013 :  18:31:21 Your proof is interesting. It shows that AE+BD+CF > 0.5(AB+BC+AC).However, as you find, this doesn't prove AE+CF+BD < AB+BC+CD.Here is a hint as to prove what you are asking:See that the triangles formed are right triangles and use the Pythagorean theorem to show that a leg (which are the altitudes) is always less than the hypotenuse.Once you show that, you can say that the sum of all three of those "legs" is less than the sum of all three of the "hypotenuses".If you need further help, please let us know.
Topic
 New Topic  Reply to Topic  Printer Friendly Jump To: Select Forum New Visitor Forum       Testing Forum Homework Help Forums       Basic Math and Pre-Algebra       Algebra       Geometry and Trigonometry       Pre-Calculus and Calculus       Probability and Statistics       Standardized Test Preparation Help       Miscellaneous Math Topics Educator Forum       Teacher Talk Parent Forum       Parent's Place  -------------------- Home Active Topics Frequently Asked Questions Member Information Search Page
 Math Forums @ Math Goodies © 2000-2004 Snitz Communications