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In the diagram, triangle BDF and triangle ECF have the same area.. If DB = 2, BA = 3, and AE = 4, find the length of line EC. Diagram is below.

 Jan 21, 2021
 #1
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EC = 7/3.

 Jan 21, 2021
 #2
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 In the diagram, triangle BDF and triangle ECF have the same area. If DB = 2, BA = 3, and AE = 4, find the length of line EC.

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BDCE is a trapezoid.     DC || BE

 

Triangles ABE and ADC are similar.

 

AB / AE = AD / AC

 

3 / 4 = 5 / AC          AC = 20 / 3

 

EC = 20 / 3 - 4             EC = 2 2/3   or  8 / 3    or       2.666666667

 Jan 21, 2021

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