We know that
triangles ADE and ABC are similar triangles
so, the ratios of their sides must be same
now, we will find value of sides
we are given
AD=12
DB=6
AE=14
EC=7
[tex]AB=AD+DB[/tex]
now, we can plug values
[tex]AB=12+6[/tex]
[tex]AB=18[/tex]
so, we can get ratio
[tex]\frac{DE}{BC} =\frac{AD}{AB}[/tex]
now, we can plug values
[tex]\frac{DE}{BC} =\frac{12}{18}[/tex]
So, the ratio in simplest form is
[tex]\frac{DE}{BC} =\frac{2}{3}[/tex]..............Answer
