Given that the enclosure area is a square of side 90 feet.
So its perimeter (P) is given by,
[tex]\begin{gathered} P=4\times Side \\ P=4\times90 \\ P=360 \end{gathered}[/tex]So the total length of the fence will be 360 feet.
It is given that a fence post is required for every 10 feet.
Then if follows that,
[tex]\begin{gathered} 10\text{ ft}\equiv1\text{ post} \\ 360\text{ ft}\equiv\frac{360}{10}=36\text{ post} \end{gathered}[/tex]Thus, there are 10 fence post required for a fenced enclosure that measures 90 feet by 90 feet.