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In triangle ABC, D is the midpoint of BC. Given that AB=3cm, AC=5cm and BC=7cm, find AD.

 Jan 16, 2021
 #1
avatar+115955 
+1

                A

     

       b                c

 

C             a                B

 

AD  is a  median  drawn from A

 

Formula for  this median length   is

 

(1/2)  sqrt  [ 2 (b^2 + c^2)   - a^2 ]   =

 

(1/2)  sqrt   [ 2 ( AC^2 + AB^2)   -  BC^2  ]  =

 

(1/2) sqrt  [  2  ( 5^2  + 3^2)  -  7^2  ]  =

 

(1/2)  sqrt [ 2 ( 34 )  - 49  ]  =

 

(1/2) sqrt  [ 68 - 49  ]   =

 

(1/2)  sqrt (19)  =  

 

sqrt (19)/2

 

 

cool cool cool

 Jan 16, 2021
edited by CPhill  Jan 16, 2021
 #2
avatar+1019 
+1

In triangle ABC, D is the midpoint of BC. Given that AB=3cm, AC=5cm, and BC=7cm, find AD.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AD = 1/2 {sqrt(2*32 + 2*52 - 72)}

 

AD = 1/2 √19  smiley

 Jan 16, 2021
edited by jugoslav  Jan 16, 2021

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