Question

A rectangular park that measures 49 yards by 42 yards will have a diagonal path built. How long will the path be? Round your answer to the nearest tenth.

Answer 1

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:

\[
\boxed{64.4} \text{ yards}
\]