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# help

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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

Apr 20, 2019
edited by Logic  Apr 20, 2019
edited by Logic  Apr 20, 2019
edited by Logic  Apr 20, 2019

#1
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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

Apr 20, 2019