We have a right triangle with legs measuring 2 units and 4 units. Using Pythagorean Theorem, the missing length (hypotenuse), x is:

\(\displaystyle{2}^{{2}}+{4}^{{2}}={x}^{{2}}\)

\(\displaystyle{4}+{16}={x}^{{2}}\)

\(\displaystyle{20}={x}^{{2}}\)

\(\displaystyle√{20}={x}\)

So, the perimeter in terms of the number of units is:

\(\displaystyle{P}={2}+{4}+√{20}={6}+√{20}\)

Since 1 unit = 8 inches, the perimeter is:

\(\displaystyle{P}={8}{\left({6}+√{20}\right)}\)

\(P \approx 83.8\) inches