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Given that [ABC]=10, find [BCD]

https://latex.artofproblemsolving.com/c/6/f/c6f8c6e18c3cdd46393c7b9a40dc8c4fb01243f6.png

 Oct 1, 2019
 #1
avatar+104962 
+2

[ ABC]  =  (1/2)AB * Height

 

10  = (1/2)*6 * Height

 

10  = 3  * Height

 

10/3  =  Height

 

So

 

[ BCD ]   =  (1/2)BD * Height

 

[BCD ]  = (1/2)(10) (10/3)

 

[BCD ]  =  5(10/3)

 

[ BCD ] =  50 / 3

 

 

cool cool cool

 Oct 1, 2019
 #2
avatar+104962 
+2

Here's one more way to solve this :

 

Triangles under the same height have the same area ratio as the ratio of their bases

 

So

 

[ BCD] / [ABC] =  10 / 6

 

[ BCD ] =  [ 10/6] [ ABC]

 

[BCD ] =  [ 10/6] [ 10]

 

[BCD ] = [ 5/3 ] [ 10]

 

[BCD ] =  50 / 3  

 

cool cool cool

 Oct 2, 2019
edited by CPhill  Oct 2, 2019

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