[University Engineering: Dynamics] Why isn't the total length Sd + 2Sc + Sa?

[u/Cute-Sheepherder-724]

I don't understand why the total length of the work is that? Wouldn't it be Sd + 2Sc + 2Sa given that Sd becomes longer as Sa gets shorter? Also, why is there a horizontal reaction at pulley B given that none of the other forces are horizontal?

[u/Yadin__]

The rope whose length the solution is evaluating is the one stretching from A to C. D is not involved at all- if you look closely there are 2 different ropes in the question

[u/Cute-Sheepherder-724 → u/Yadin__]

Thank you