Answer:
CD = 47.2 units
Step-by-step explanation:
Given:-
- L is the mid-point of line segment CD
- Where,
CL = 13x + 8
LD = 23x - 4
Find:-
Find the length of segment CD.
Solution:-
- Since the point L is the midpoint of the CD then two expressions given CL and LD must add up to CD.
CD = CL + LD
CD = (13x + 8) + (23x - 4)
CD = 36x + 4
- To determine the value of x we can also say that CL and LD must be equal because L is the common mid-point on the line segment CD. So we can write:
CL = LD
13x + 8 = 23x - 4
12 = 10x
x = 1.2 units
- Now substitute the value of x in the expression developed for CD as follows:
CD = 36*(1.2) + 4
CD = 43.2 + 4
CD = 47.2 units
