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.
+130066 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
