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If CE:EA:AD:DB=2:3:4:5, then what is [ACD]/[ABE]?

 Jan 24, 2021
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If   CE  : EA  = 2 : 3

 

Then    the  altitude of triangle  ABE  =  3 / (3 + 2)    = 3/5  the altitude of triangle  ACD

 

And if   AD : DB   =  4 :  5  

 

Then  the base of triangle   ABE  to  the base of triangle  ACD =  (4 + 5) / 4  =   (9/4)

 

Call the area of triangle ACD  =(1/2) A * B         where A is the altitude and  B  is the  base

 

And the area of triangle ABE  = (1/2) ( 3/5)A  * ( 9/4) B  =  (1/2) (27/20) AB

 

So

 

[ACD]  / [ ABE ]  =     (1/2) AB  /  {(1/2) AB  (27/20) ]  =     1 / (27/20)  =   20 /27

 

 

cool cool cool

 Jan 24, 2021

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