Idk what to do next. show working too.

BC is 9 units long

Work Shown:

Let x be the length of segment BC.

BC is parallel to DE, so this means that triangle ABC is similar to triangle ADE.  

Side AB pairs with side AD (both are horizontal sides of triangle ABC and triangle ADE respectively)

Side BC pairs with side DE (both are vertical sides of triangle ABC and triangle ADE respectively)

Because of those facts above, we can end up with this proportion

AB/AD = BC/DE

Let's plug in the given values and isolate x

AB/AD = BC/DE

12/20 = x/15

12*15 = 20*x ... cross multiply

180 = 20x

20x = 180

20x/20 = 180/20 ... divide both sides by 20

x = 9

Segment BC is 9 units long.

note: There is no need to calculate the length of segment AE. Though you are correct in stating that AE = 25.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.