A carpenter is cutting a triangular plywood panel ABC. He marks D on the edge AB and E on the edge AC and saws along DE, keeping DE parallel to BC. His marks give AD = 21 cm and DB = 14 cm, and the edge AC is 45 cm long. How far from A does the cut meet AC, that is, what is AE (in cm)?

Question

Accepted Answer

27. Because the cut DE is parallel to BC, AE : EC = AD : DB = 21 : 14 = 3 : 2. So AC = 45 cm splits into 3 + 2 = 5 parts of 9 cm, giving AE = 3 × 9 = 27 cm and EC = 18 cm. The answer 18 is EC, measured from the wrong end; 30 comes from applying 2/3 straight to AC, using the part-to-part ratio where a part-to-whole ratio is needed; 22.5 halves AC.

A carpenter is cutting a triangular plywood panel ABC. He marks D on the edge AB and E on the edge AC and saws along DE, keeping DE parallel to BC. His marks give AD = 21 cm and DB = 14 cm, and the edge AC is 45 cm long. How far from A does the cut meet AC, that is, what is AE (in cm)?

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