As the picture highlights, the opposite sides have the same lengths. The perimeter is the sum of all lengths, so we have
[tex] P = 2(2s-5) + 2(4s-13) [/tex]
Plug the required value for the perimeter and expand the right hand side:
[tex] 108 = 4s-10 + 8s-26 [/tex]
Simplify the right hand side:
[tex] 108 = 12s-36 [/tex]
Add 36 to both sides:
[tex] 144 = 12s [/tex]
Divide both sides by 12:
[tex] 12 = s [/tex]
Now that we know the value for s, let's deduce the lengths of the sides:
[tex] 2s-5 = 2\cdot 12 - 5 = 24-5 = 19 [/tex]
[tex] 4s-13 = 4\cdot 12 - 13 = 48-13 = 35 [/tex]
