Answer:
[tex]16\ \text{miles}[/tex]
Step-by-step explanation:
In a parallelogram the diagnols bisect each other. So,
[tex]DE=EB\\\Rightarrow y+2=3y-4\\\Rightarrow 4+2=3y-y\\\Rightarrow 6=2y\\\Rightarrow y=\dfrac{6}{2}\\\Rightarrow y=3[/tex]
[tex]DE=y+2\\\Rightarrow DE=3+2\\\Rightarrow DE=5[/tex]
[tex]BD=2DE\\\Rightarrow BD=2\times 5\\\Rightarrow BD=10[/tex]
[tex]EC=2y-3\\\Rightarrow EC=2\times 3-3\\\Rightarrow EC=3[/tex]
[tex]AC=2EC\\\Rightarrow AC=2\times 3\\\Rightarrow AC=6[/tex]
The sum of the diagonals is [tex]BD+AC=10+6=16\ \text{miles}[/tex]
The sum of the lengths of the two trails is [tex]16\ \text{miles}[/tex].
