+1206 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?
+9519 What is m and n? The problem is still not complete!
Please mind what you are posting, do not just copy from some website and throw it here.
At least check if there are any mistakes in the problem before posting... *facepalm*
+9466 In order for ∠A to be the largest angle, It must be that the side formed by ∠A is the largest side. So...
| 3x < x + 9 | |
| 2x < 9 |
|
| x < \(\frac92\) |
But by the triangle inequality theorem,
| x + 9 < ( 3x ) + ( x + 4 ) | |
| x + 9 < 3x + x + 4 |
|
| 9 < 3x + 4 | |
| 5 < 3x |
|
| \(\frac53\) < x |
So in order for ∠A to be the largest angle, it must be that \(\frac53
The least possible value of n - m is \(\frac92-\frac53\ =\ \frac{27}{6}-\frac{10}{6}\ =\ \boxed{\frac{17}{6}}\)
( Here's an older answer for this question: https://web2.0calc.com/questions/geometry-question. . .#r5 )
