Final answer:
CD is found to be 12 units long by setting up and solving the equation 3x = x + 8, as C is the midpoint of BD, and therefore BC equals CD.
Step-by-step explanation:
To determine the length of CD when C is the midpoint of BD, we know that BC is equal to CD since the midpoint of a segment divides it into two segments of equal length. Given BC = 3x and CD = x + 8, since those two lengths must be equal, we can set up an equation to solve for x. The equation would be 3x = x + 8.
To solve for x, we subtract x from both sides, getting 2x = 8 and then divide both sides by 2 to find that x = 4. Now that we know x we can substitute it back into the equation for CD to find CD. Since CD = x + 8 we substitute x to find CD = 4 + 8, which means CD equals 12.