This week's puzzle will involve the travels of space pioneer Trig O'Nometry as he checks out the new hydroponics modules that were recently completed at moon base Armstrong. There are three modules: Alpha, Beta, and Gamma. All three are connected by tunnels that are straight and whole numbers in length. Trig hopped into the transport rover in Alpha Pod and was supposed to go to Gamma Pod. By mistake he went to Beta Pod which is closer to Alpha Pod and exactly 12 kilometers from the tunnel connecting Alpha to Gamma. When Trig finally arrives at the Gamma Pod he has traveled a total of 35 kilometers. What is the length of the tunnels connecting the three hydroponics pods?
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