First, let's calculate the length of the hypotenuse, using the Pythagorean theorem.
This theorem states that the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} c^2=12^2+35^2\\ \\ c^2=144+1225\\ \\ c^2=1369\\ \\ c=37 \end{gathered}[/tex]
Now, calculating the perimeter, we have:
[tex]P=37+35+12=84\text{ ft}[/tex]
Let's convert the perimeter to inches:
[tex]P=84\text{ ft}=84\cdot12\text{ in}=1008\text{ in}[/tex]
Calculating the number of fences, we have:
[tex]\frac{1008}{14}=72[/tex]
Therefore 72 fence posts will be needed.
