Final answer:
The length of segment SD is 136 units.
Step-by-step explanation:
To find the length of segment SD, we need to find the sum of SM and MD. We are given that SM = 12x - 4 and MD = 6x + 32. To find the value of x, we can set SM equal to MD and solve for x.
12x - 4 = 6x + 32
Subtracting 6x from both sides: 6x - 4 = 32
Adding 4 to both sides: 6x = 36
Dividing both sides by 6: x = 6
Now that we have the value of x, we can substitute it back into the equations:
SM = 12(6) - 4 = 68
MD = 6(6) + 32 = 68
The length of segment SD is the sum of SM and MD:
SD = SM + MD = 68 + 68 = 136