A tailor cuts a triangular flag ABC and stitches a ribbon across it from a point D on the edge AB to a point E on the edge AC, keeping the ribbon parallel to BC. She places D so that AD = 12 cm, while the full edge AB measures 32 cm. If the edge AC is 40 cm long, how far from the corner C does the ribbon meet AC, that is, what is EC (in cm)?

Question

Accepted Answer

25. Since the ribbon DE is parallel to BC, AE/AC = AD/AB = 12/32 = 3/8. So AE = 3/8 × 40 = 15 cm, and the distance from C is EC = 40 − 15 = 25 cm. The answer 15 is AE, measured from the wrong corner; 20 assumes the ribbon is a midline of the triangle; 16 comes from using AD : DB = 12 : 20 = 3 : 5 in place of AD : AB, giving AE = 24 and EC = 16 — the standard part-to-part versus part-to-whole slip.

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