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

 

 Apr 25, 2019
 #1
avatar+104882 
+1

We have that either

 

x + 4 + 3x > x + 9         or      3x + x + 9 > x + 4        or      x + 4 + x + 9 > 3x

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

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

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

 

Taking the most restrictive interval

 

 

5/3 < x < 13

 

So

 

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

 

 

cool cool cool

 Apr 25, 2019

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