#### Answer

Estimate: $105$ feet
Exact: $104\frac{5}{8}$ feet

#### Work Step by Step

We know that the perimeter is given by:
$Perimeter=side_1+side_2+side_3+side_4$
Thus:
$side_4=Perimeter-side_1-side_2-side_3$
We plug in the given values:
$side_4=518\frac{3}{4}-108\frac{1}{4}-162\frac{3}{8}-143\frac{1}{2}$
First, we estimate by rounding:
$side_4=519-108-162-144=105$ feet
Next, we get the exact answer:
$side_4=518\frac{3}{4}-108\frac{1}{4}-162\frac{3}{8}-143\frac{1}{2}$
$side_4=518\frac{6}{8}-108\frac{2}{8}-162\frac{3}{8}-143\frac{4}{8}$
$side_4=(518-108-162-143)+(\frac{6}{8}-\frac{2}{8}-\frac{3}{8}-\frac{4}{8})$
$side_4=(105)-\frac{3}{8}$
$side_4=104+\frac{8}{8}-\frac{3}{8}$
$side_4=104\frac{5}{8}$ feet