Question

Use this figure to find each ratio in simplest form.

Answer 1

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

$AB=AD+DB$

now, we can plug values

$AB=12+6$

$AB=18$

so, we can get ratio

$\frac{DE}{BC} =\frac{AD}{AB}$

now, we can plug values

$\frac{DE}{BC} =\frac{12}{18}$

So, the ratio in simplest form is

$\frac{DE}{BC} =\frac{2}{3}$..............Answer