A triangular field ABC has AB = 18 m and AC = 27 m. A straight footpath from A runs along the bisector of angle A and meets the far boundary BC at D. The part BD measures 12 m. How long is DC (in m)?

Question

Accepted Answer

18. The bisector splits BC in the ratio of the two enclosing sides: BD/DC = AB/AC = 18/27 = 2/3. So 12/DC = 2/3 and DC = 18 m. The value 8 comes from inverting the proportion (DC = 12 × 18/27); 12 comes from assuming the bisector is also a median so DC = BD; 9 is just AC − AB, which has nothing to do with the split.

A triangular field ABC has AB = 18 m and AC = 27 m. A straight footpath from A runs along the bisector of angle A and meets the far boundary BC at D. The part BD measures 12 m. How long is DC (in m)?

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