Final answer:
BD can be calculated by adding the lengths of BC and CD. Upon calculating, BD is found to be x + 29, which is not represented by any of the given answer choices, making the correct answer 'None of the above'.
Step-by-step explanation:
If BC = 12, CD = x + 17, and BD = 2x + 13, we must find the value of BD, given the segments are parts of the same line. Since BD is the entire length from B to D, we can express it as the sum of BC and CD, which gives us BD = BC + CD.
Substituting the known values, we get BD = 12 + (x + 17). To find the expression for BD, we combine the constants: BD = x + 29.
Reviewing the provided answer choices, it appears that there may have been a typo as none of the options match our expression for BD, so the correct answer is 'None of the above'.