Question

B.C.D依次是线段上A.E的三点,已知A,E=9,BD=3,则图中以A,B,C,D,E这5个点为端点的所有线段长度之和

Answer 1

(1)以A为起点的线段：AB+AC+AD+AE;

(2)以B为起点的线段：BC+BD+BE;

(3)以C为起点的线段：CD+CE;

(4)以D为起点的线段：DE;

设AB=X1,BC=X2,CD=X3,DE=X4

则(1)式=4X1+3X2+2X3+X4;

(2)式=3X2+2X3+X4;

(3)式=2X3+X4;

(4)式=X4;

(1)+(2)+(3)+(4) = 4X1+6X2+6X3+4X4=4(X1+X2+X3+X4)+2(X2+X3)=4AE+2BD=42;