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.
Find the length of line EC.
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\(\frac{3(5+x)}{2}-A_{ECF}=\frac{5(3+2)}{2}-A_{BDF}\\ A_{ECF}=A_{BDF}\\ 15+3x=25\\ x=\frac{10}{3}=3\frac{1}{3}\\ \color{blue}\overline{EC}=3\frac{1}{3}\\\)
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