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D is on side AC of Triangle ABC. We know [ABC] = 120, AD = 8, DC = 3. What is [ABD]?

 Jul 22, 2021
 #1
avatar+1486 
+2

D is on side AC of Triangle ABC. We know [ABC] = 120, AD = 8, DC = 3. What is [ABD]?

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Let ΔABC be the right triangle.

 

If AD = 8, DC = 3, and [ABC] = 120, then AB = 21 9/11

 

[ABD] = 1/2(AD * AB) = 87 3/11 square units

 Jul 22, 2021
edited by jugoslav  Jul 22, 2021
 #2
avatar+121054 
+1

Triangles   ABD    and   CBD  will  be  under  the  same  height

 

So     [ABD]  =    (8 / ( 3 + 8) )  *  120   =   (8)(120)  /11  = 960/11    ≈  87.27

 

cool cool cool

 Jul 22, 2021
edited by CPhill  Jul 22, 2021

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