To find the length of the diagonal path in a rectangular park, you can use the Pythagorean theorem. The formula is:
\[ d = \sqrt{l^2 + w^2} \]
where \(d\) is the length of the diagonal, \(l\) is the length of the rectangle, and \(w\) is the width.
In this case:
- Length \(l = 49\) yards
- Width \(w = 42\) yards
Substituting the values into the formula:
\[ d = \sqrt{49^2 + 42^2} \]
Calculating \(49^2\) and \(42^2\):
\[ 49^2 = 2401 \] \[ 42^2 = 1764 \]
Now, add these values together:
\[ d = \sqrt{2401 + 1764} \] \[ d = \sqrt{4165} \]
Now calculate the square root:
\[ d \approx 64.4 \text{ yards} \]
Thus, the length of the diagonal path, rounded to the nearest tenth, is approximately:
\[ \boxed{64.4} \text{ yards} \]