同一线段AB上C,D两点,已知AD=9/5BD,AC=5/9CB,CD=4cm,则AB的长为多少

题目

同一线段AB上C,D两点,已知AD=9/5BD,AC=5/9CB,CD=4cm,则AB的长为多少

答案

∵AD=9/5BD ==>AC+CD=9/5BD
==>AC+4=9/5BD (CD=4cm)
==>9/5BD-AC=4.(1)
AC=5/9CB ==>AC=5/9(CD+BD)
==>AC=5/9CD+5/9BD
==>AC=20/9+5/9BD (CD=4cm)
==>AC-5/9BD=20/9.(2)
解方程组(1)和(2)得AC=BD=5
∴AB=AC+CD+BD=5+4+5=14cm.