L is the midpoint of segment CD. If CL = 1/3x+8 and LD = 2/3x-4, find the length of segment CD.

Answer 1

Since L is the midpoint, then CL must be the same length as LD. So set the two expressions equal to each other and solve for x. Then using our newly found x, we can find length CD.

(1/3)x + 8 = (2/3)x -4

add -(1/3)x to both sides

8 = (1/3)x - 4

add 4 to both sides

12 = (1/3)x

multiply both sides by 3

36 = 1x or x = 36

Now plug 36 into each of the expressions

CL = (1/3)(36) + 8 = 12 + 8 = 20

LD = (2/3)(36) - 4 = 24 - 4 = 20

Notice they are both the same length because L is the midpoint (is in the middle of segment CD)

Length of CD = 20 + 20 = 40