Final answer:
To find the value of CD, we need to find the value of x first by using the midpoint formula. After solving for x, we substitute it back into the expression for CD to find its value.
Step-by-step explanation:
To find the value of CD, we need to find the value of x first. Given that D is the midpoint of CE, we can use the midpoint formula: CD = (1/2)CE. Substituting the values, we have (10x) = (1/2)(16x + 16). We can solve for x by multiplying both sides of the equation by 2 and then solving the resulting linear equation.
x = (1/2)(16x + 16)/10
x = (16x + 16)/20
20x = 16x + 16
4x = 16
x = 4
Now that we have the value of x as 4, we can substitute it back into the expression for CD: CD = 10x = 10(4) = 40
Therefore, the value of CD is 40. Option d) 16x is not correct.