Answer:
4.5 mm
Explanation:
You want the length of AB in similar triangles ACE and BCD, given BD is parallel to AE, and AC=36 mm, ED=9 mm, EC=72 mm.
Proportion
Corresponding segments in the two triangles are proportional, so we have ...
AB/ED = AC/EC
AB/(9 mm) = (36 mm)/(72 mm) = 1/2
AB = (9 mm)(1/2) = 4.5 mm . . . . . multiply by 9 mm
The length of segment AB is 4.5 mm.