Answer:
BE=7 un., EC=5 un.
Step-by-step explanation:
Triangles ABC and ADE are similar, then
[tex]\dfrac{14}{14-x}=\dfrac{12}{BE}=\dfrac{10}{x}.[/tex]
Thus,
[tex]14x=10(14-x),\\ \\14x=140-10x,\\ \\24x=140,\\ \\x=\dfrac{140}{24}=\dfrac{35}{6}\ un..[/tex]
Therefore,
[tex]\dfrac{12}{BE}=\dfrac{10}{\frac{35}{6}},\\ \\10BE=12\cdot \dfrac{35}{6},\\ \\10BE=70,\\ \\BE=7\ un.[/tex]
So [tex]EC=BC-BE=12-7=5\ un.[/tex]
