18. As shown in the figure, in △ABC, the middle vertical line DE of BC intersects BC at point D and AB at point E. If the perimeter of △EDC is 24 and the difference between the perimeter of △ABC and the perimeter of quadrilateral AEDC is 12, the length of line segment de is 6.

Solution:

The circumference of ABC =AB+AC+BC=AE+BE+BD+DC.

Quadrilateral AEDC perimeter =AE+ED+CD+AC

The perimeter of ABC-the perimeter of the quadrilateral AEDC = 12.

(AE+BE+BD+DC)-(AE+ED+CD+AC)= 12

BE+BD-ED= 12 ( 1)

∵△ perimeter of ∵△EDC =EC+ED+CD=24

EC = BE CD = BD。

∴BE+ED+BD=24 (2)

∴( 1)+ (2)

BE+BD= 18

∴ed = be+BD- 12 = 18- 12 = 6