To solve this, let's break it down geometrically.

The farmer built three sections of a fence:

• The first section is along the diagonal, labeled $L = 20.00\ \text{m}$.
• The second section is vertical, labeled $L = 20.00\ \text{m}$.
• The third section is horizontal, labeled $L/2 = 10.00\ \text{m}$.

Task: Find the straight-line distance $d$ the farmer has to walk back to the starting point.

This forms a triangle where:

• One side is $L$ (the diagonal),
• One vertical side is $L$,
• The horizontal side is $L/2$.

Now, to calculate the distance $d$, we apply the Pythagorean theorem. The diagonal forms the hypotenuse of the right triangle where:

• The vertical side is $L - L = 20.00 - 20.00 = 0$.