如图所示.A2,A3是线段A1A4上两点,且A1A2=a1,A1A3=a2,A1A4=a3.求线段A1A4上所有线段之和.
问题描述:
如图所示.A2,A3是线段A1A4上两点,且A1A2=a1,A1A3=a2,A1A4=a3.求线段A1A4上所有线段之和.
答
A2A3=A1A3-A1A2,A2A4=A1A4-A1A2,A3A4=A1A4-A1A3,
∴线段A1A4上所有线段之和=3A1A4-A1A2+A1A3=3a3-a1+a2.
即所有的线段之和为:3a3-a1+a2.