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The incircle of radius 4 of a triangle ABC touches the side BC at D. If BD=6, DC=8, then what is the area of triangle ABC?

 Jan 5, 2021
 #1
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The answer is 84 don't have any time for an explanation today. Hope this is correct. 

 Jan 5, 2021
edited by Guest  Jan 5, 2021
 #2
avatar+1164 
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Yes, it is 84!

Find angles A, B, and C

Find side lengths

Use Heron's formula to calculate the area.

jugoslav  Jan 5, 2021
 #3
avatar+117576 
+1

See the image here :

 

 

The  perimeter of the  triangle is  ( 6 + 8)  + (6 + 7)  + ( 8 + 7)  =  14 + 13 + 15  =  42

 

The area  =  (1/2) radius of incircle  * perimeter  = 

 

(1/2) (4) (42)  = 

 

2 *  42  =  

 

84    .....just as the  guest found  !!!!

 

 

cool cool cool

 Jan 5, 2021

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