As shown in the figure, take a point D on AB, take a point C on the extension line of AB, so that BD = 1 / 3AB = 1 / 4bc, and the midpoint of line AB and BC are m, n respectively, Mn = 7cm, Finding the length of line AB, CD

A——M—D——B——N——C
∵BD＝1/3AB＝1/4BC
∴AB＝3BD,BC＝4BD
∵ m is the midpoint of ab
∴BM＝1/2AB＝3/2BD
∵ n is the midpoint of BC
∴BN＝1/2BC＝2BD
∴MN＝BM+BN＝3/2BD+2BD＝7/2BD
∴7/2BD＝7
∴BD＝2
∴AB＝3BD＝6（cm）
CD＝BC+BD＝5BD＝10(cm)
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