+0  
 
-3
60
1
avatar+48 

1. Let \(n\) be a positive integer. In triangle \(ABC,AB = 3n, AC = 2n + 15, BC = n + 30,\)  and \(\angle A > \angle B > \angle C\). How many possible values of \(n\) are there?

 

2. Triangle \(ABC\) has altitudes  \(\overline{AD}, \overline{BE},\) and \(\overline{CF}\) If  \(AD = 12, BE = 14,\) and \(CF\) is a positive integer, then find the largest possible value of \(CF.\)

 Mar 30, 2020
 #1
avatar
0

1. n can be 9, 10, 11, 12, for four possible values of n.

 

2. Let h be the third altitude.  Then by the triangle inequality, h + 12 > 14, h + 14 > 12, and 12 + 14 > h.  The largest integer h that satisfies these inequalities is h = 25.

 Mar 31, 2020

26 Online Users

avatar
avatar
avatar