To determine the walking distance saved, we need to compare the distance of the path that cuts across the lot (the dashed line, representing the hypotenuse of a triangle) with the total distance of the path around the lot (the sum of the two sides of the triangle).

The details provided indicate:

• The length of one side is 34 feet.
• The other side is represented as x + 4.
• The hypotenuse is represented as x.

Steps:

1. Using the Pythagorean theorem: $\text{Hypotenuse}^2 = \text{Side}_1^2 + \text{Side}_2^2$ Substituting: $x^2 = 34^2 + (x + 4)^2$

2. Expand and simplify: $x^2 = 1156 + (x^2 + 8x + 16)$ $x^2 = x^2 + 8x + 1172$

3. Eliminate $x^2$ from both sides: $0 = 8x + 1172$

4. Solve for $x$: $8x = -1172 \quad \rightarrow \quad x = -146$

If $x = -146$ is unintended or additional values are missing, clarify the context.

Would you like me to clarify?