ABCD is a trapezium with AB parallel to DC. A straight line EF is drawn parallel to AB, meeting the leg AD at E and the leg BC at F, so that AE : ED = 2 : 3. If BC = 20 cm, find BF (in cm).

EF parallel to AB cuts the legs in the same ratio, so BF : FC = AE : ED = 2 : 3. The 20 cm of BC therefore splits into 2 + 3 = 5 equal parts of 4 cm each, and BF = 2 parts = 8 cm. The answer 12 is FC, the other part; 10 assumes E and F are midpoints; 4 stops at the size of one part without multiplying by 2.