+0  
 
0
1
1
avatar+1636 

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

 Jun 9, 2024
 #1
avatar+129401 
+1

Find the area with Heron's Formula

semi-perimeter = 17

 

Area =  sqrt [ 17 * 2 * 7 * 8 ]  = 4sqrt 119

 

The shortest altitude is drawn to the longest side....so....

 

4sqrt119 = (1/2)  15  * altitude

 

altitude  =  4/ 7.5  * sqrt 119  =   4 / (15/2) * sqrt 119  =  (8/15)sqrt 119

 

cool cool cool

 Jun 9, 2024

6 Online Users

avatar
avatar
avatar