ABCD is a trapezium with AB parallel to DC. A point E is taken on the leg AD and a point F on the leg BC so that EF is parallel to AB. Given AE = 3.6 cm, ED = 2.4 cm and BF = 4.5 cm, find FC (in cm).

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Accepted Answer

3. EF is parallel to AB and hence to DC, so it cuts the two legs proportionally: AE/ED = BF/FC. Here 3.6/2.4 = 1.5, so 1.5 = 4.5/FC and FC = 3 cm. Choosing 6.75 means the proportion was inverted (FC = 4.5 × 3.6/2.4); 4.5 assumes F is the midpoint of BC so FC = BF; 2.4 simply copies ED, matching the wrong pair of segments.

ABCD is a trapezium with AB parallel to DC. A point E is taken on the leg AD and a point F on the leg BC so that EF is parallel to AB. Given AE = 3.6 cm, ED = 2.4 cm and BF = 4.5 cm, find FC (in cm).

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