Answer
$21.9$ yards.
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the width and $2x$ the length of the rectangle.
Step 2. Using the Pythagorean's Theorem in the right triangle involving the diagonal, we have $(2x)^2+x^2=64^2$ or $5x^2=64^2$, which gives $x=\frac{64\sqrt 5}{5}\approx28.62$ yards.
Step 3. Walking diagonally will save $3\times28.62-64\approx21.9$ yards.
