Question

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

Answer 1

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

Answer 2

 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