Final answer:
The length of IK is 47 units.
Step-by-step explanation:
Given that point D is the midpoint of IK, we know that the distance from I to D is equal to the distance from D to K. Let's set up an equation to solve for x.
ID = DK
17x - 4 = 8x + 23
Now, we can solve for x. Subtracting 8x from both sides and adding 4 to both sides, we get:
9x = 27
x = 3
Now, we substitute the value of x back into the expressions for ID and DK to find the length of IK:
ID = 17x - 4 = 17(3) - 4 = 47
DK = 8x + 23 = 8(3) + 23 = 47
Therefore, the length of IK is 47 units.