已知线段AB,延长AB到C,使BC=(2/3)AB,反向延长AB到D,使AD=(3/2)AB到D,E是线段DC中点,若AE=2cm,求线段AB长.

Question

已知线段AB,延长AB到C,使BC=(2/3)AB,反向延长AB到D,使AD=(3/2)AB到D,E是线段DC中点,若AE=2cm,求线段AB长.

Answer 1

设AB=3X,则AC=5X,AF=3X,AD=3X+(3/2)X=(9/2)X,则CD=AD+AC=(19/2)X,
那么可得DE=(1/2)DC=(19/4)X>AD,可则E点在A点的右侧,
则AE=DE-AD=(1/4)X=2cm,
由此可得X=8cm,那么AB=3X=24cm