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In the diagram, triangle BDF and triangle ECF have the same area.. If DB = 2, BA = 3, and AE = 5, find the length of line EC. Diagram is below.

 

 Feb 12, 2022
 #1
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Because   ABFE  = ABFE  and  triangle  BDF  =  triangle  ECF

 

Then  right triangle ADE   must have the same area as triangle  ABC

 

Area of triangle BDF  = (1/2)(DB + BA) ( AE)  =   (1/2) (2 + 3)  ( 5) =   12.5

 

Since triangle  ECF  has the same area we  have that

 

(1/2)  ( BA )  ( AE  + EC )   =12.5     multiply both sides by 2

 

(BA) ( AE +  EC)  = 25

 

(3)   ( 5 + EC)  =  25      divide both sides by 3

 

EC + 5  = 25/3

 

EC  =   25/3   - 5

 

EC  =  25/3  = 15/3   =    10/3

 

 

cool cool cool

 Feb 12, 2022

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