Let ABCD be a parallelogram and E be the midpoint of BC. The diagonal BD and line segment AE intersects at F. If BF = 2·4 cm, then what is BD equal to?

In parallelogram ABCD, E is midpoint of BC. AE and BD intersect at F. Triangles AFD and EFB are similar (AA, since AD ∥ BC). AD/EB = AD/(BC/2) = 2. So DF/FB = AD/EB = 2, meaning DF = 2·BF = 2(2.4) = 4.8 cm. So BD = BF + FD = 2.4 + 4.8 = 7.2 cm.