Question

已知线段AB=5cm,延长AB到C,使AC=7cm,在AB的反向延长线上取点D,使BD=4BC 设线段CD的中点为E

问线段AE是线段CD的几分之一

Answer 1

∵ BC = AC - AB = 7 - 5 = 2
∴ BD = 4BC = 4 × 2 = 8
∴ DA = BD - AB = 8 - 5 = 3
∴ CD = DA + AC = 3+ 7 =10
∵ E是CD的中点
∴ DE = CD÷2 = 10÷2 = 5
∴ AE = DE - DA = 5 - 3 = 2
AE÷CD = 2÷10 =1/5
线段AE是线段CD的五分之一。

Answer 2

∵ BC = AC - AB = 7 - 5 = 2
∴ BD = 4BC = 4 × 2 = 8
∴ DA = BD - AB = 8 - 5 = 3
∴ CD = DA + AC = 3+ 7 =10
∵ E是CD的中点
∴ DE = CD÷2 = 10÷2 = 5
∴ AE = DE - DA = 5 - 3 = 2
AE÷CD = 2÷10 =1/5
线段AE是线段CD的五分之一。