In the triangle shown, for \(\angle A\) to be the largest angle of the triangle, it must be that m . What is the least possible value of \(n-m\),expressed as a common fraction?

sorry I dont know why the problem is doing that here is what that odd "m" stands for. m < x < n

Logic Apr 20, 2019

#1**+1 **

OK.....no prob....I think I see what we need...

If A is the greatest angle, then BC is the greatest side........so.... we have these possible inequalities

x + 9 < (3x) + (x + 4) and (3x )+ (x + 9 ) > x + 4 or (x + 4) + (x + 9) > 3x

x + 9 < 4x + 4 4x + 9 > x + 4 2x + 13 > 3x

5 < 3x 3x > -5 13 > x

5/3 < x x > -5/3 x < 13

We must take the smallest intherval for our answers....this is

5/3 < x < 13

So

n - m = 13 - 5/3 = 39/3 - 5/3 = 34 / 3

CPhill Apr 20, 2019