Question

The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment AB meets segment CD at E. Find the length of segment AE.

Answer 1

`(5√(5))/(3)`

Explanation:

Extend DC to F. Triangle FAE and DBE are similar with ratio 5:4. Thus, AE=(5AB)/9, AB=
`√(3^2+6^2) =√(45) =3√(5)` and
`AE=(5(3√(5)))/(9)` which can be simplified to
`(5√(5))/(3)`.

Hope this helped! :)

Answer 2

`(5√(5) )/(3)`