Question

In the diagram, BC¯¯¯¯¯∥DE¯¯¯¯¯ .

What is AE ?

Answer 1

So there are two triangles here: Smaller one (ADE) and bigger one (ABC) and they both are similar.

So you can use proportions here.

AB / AC = AD / AE

AB = AD + DB = 6 + 1 = 7
AC = AE + 3

AD = 6

So plug in these values:

AB / AC = AD / AE becomes
7 / (AE + 3) = 6 / AE

Now do the cross multiply:

7 AE = 6 (AE + 3)

Now solve for AE:

7AE = 6AE + 18

AE = 18