Processing math: 100%
 
+0  
 
-3
632
1
avatar+87 

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

 

2. Triangle ABC has altitudes  ¯AD,¯BE, and ¯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

2 Online Users

avatar