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Perimeter is the outside dimensions.
There are two sides 5z and two sides 4z +3.
5z +5z +4z+3 + 4z +3 = 186
Combine like terms:
18z + 6 = 186
Subtract 6 from both sides:
18z = 180
Divide both sides by 18:
z = 180 / 18
z = 10