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In the triangle shown, for angle A to be the largest angle of the triangle, it must be that m

 

diagram

 Jan 29, 2019
edited by Guest  Jan 29, 2019
 #1
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It must be that    x + 9 is the longest side since the longest side of a triangle is opposite the largest angle

 

So

 

x + 9 > 3x               

 

9 > 2x

 

9/2 > x

 

And   x + 9 will always be greater than x + 4

 

But we also  have the restriction (by the Triangle Inequalty) that

 

3x + (x + 4) > x + 9

 

4x + 4 > x + 9

 

3x > 5

 

x > 5/3

 

So....the allowable values for x that make x + 9  the longest side  are

 

5/3 < x < 9/2

 

 

cool cool cool

 Jan 29, 2019

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