Find AE (in cm), where the bisector of angle B in triangle ABC meets the opposite side AC at E, and AB = 4.5 cm, BC = 7.5 cm and AC = 8 cm.

The bisector from $B$ divides $AC$ in the ratio of the sides enclosing angle $B:\frac{AE}{EC}=\frac{AB}{BC}=\frac{4.5}{7.5}=\frac{3}{5}$. The 8 cm of $AC$ therefore splits into 3 + 5 = 8 parts of 1 cm each, so $AE=3$ cm (and $EC=5$ cm). The value 5 answers for $EC$, the wrong part; 4 assumes $E$ is the midpoint of $AC$; 4.5 copies $AB$, mistaking a side of the triangle for the piece cut off on $AC$.