Answer
$24.4$ yards.
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the width of the rectangle.
Step 2. Using the Pythagorean's Theorem in the right triangle, we have $(3x)^2+x^2=92^2$ or $10x^2=92$, which gives $x\approx29.093$ yards
Step 3. Thus, walking diagonally will save $4(29.093)-92\approx24.4$ yards.
