Math Is Fun Forum

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Triangle funnes agggh

In the triangle shown, n is a positive integer, and \angle A > \angle B > \angle C. How many possible values of n are there?

theres a figure but im new so I cant post wahh
The sides are AB = 4n-9, BC = 3n+4, AC = 3n+1.
I figured out BC is the biggest and AC is second and AB is third biggest. pls help. thx a ton!!!!!:D

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Triangle funnes agggh

hi thedarktiger,

In any triangle with sides p, q and r

p + q > r

If you use this three times, taking a different side as r each time, then you will get inequalities involving n.

Also, the minus in the expression for AB leads to a fourth inequality.

All must be true so pick the most limiting which will give a lower bound.

Then you have the inequalities on the sides which will give an upper bound.

Bob

Last edited by Bob (2014-01-15 21:08:47)

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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

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: Triangle funnes agggh

Oh thanks Im so stupid I thought something was wrong with the problem! Thx so much

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Triangle funnes agggh

Oh that's not so stupid.  I worked out the triangle inequality results and totally forgot the BC > AC > AB ones.  It was only when I looked at your quadrilateral post that it occurred to me that I'd left out half the information. 

As for the quad problem:

It's a tough one if the points make a random quad.  But once you realise three points are in a straight line it becomes easier.  So maybe that was deliberate?

Taking the two problems together it looks like the book is testing the triangle inequality in both so it begins to make sense.

Bob

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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