Question

L is the midpoint of segment CD. If CL=13x+8 and LD=23x−4 , find the length of segment CD.

Answer 1

CD= cl+ld CD= (1/3)x + 8 + (2/3)x - 4 CD= (1/3)(36) + 8 + (2/3)(36) - 4 CD= 12 + 8 + 24 - 4 CD= 40

Answer 2

CD = 47.2 units

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