Line goes from one vertex of rectangle to half of other side rule

Question

this question was on my test and I don't know which rule to apply to solve. ABCD is a rectangle. Lines goes from A to half of other side and another line goes from D to half of other side OL is 2 cm. What is AO? An image is inserted below.

Answer 1

Let $M$ be the midpoint of $\overline{AL}$. Then $\triangle{OLD}\sim\triangle{OMK}$, so $DL:KM::OL:OM$. By construction, $DL=\frac12DC$, $KM=\frac34CD$, and of course $AM=OM+OL$. I trust that you can complete the calculation from here.