Final answer:
Upon setting the expressions for WX and XY equal to each other, solving for x, and substituting back into the expression for WX, we find that WX equals 74 units, which does not match any of the multiple-choice answers provided.
Step-by-step explanation:
If X is the midpoint of WY, then the lengths of WX and XY are equal. Given that WX = 12x + 26 and XY = 20x - 6, we can set these two expressions equal to each other to find the value of x.
The equation then is:
12x + 26 = 20x - 6.
Subtract 12x from both sides of the equation:
26 = 8x - 6.
Add 6 to both sides of the equation:
32 = 8x.
Divide both sides by 8:
x = 4.
Now that we have the value of x, we can substitute it back into the expression for WX to find its length:
WX = 12(4) + 26 = 48 + 26 = 74. Since this is not an option in the multiple-choice answers, there must be an error in the question or the provided options. According to the calculations, WX is 74 units long, not one of the provided choices a, b, c, or d.