Question

A rectangular park that measures 33 yards by 58 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, we can use the Pythagorean theorem. According to this theorem, for a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.

The lengths of the sides of the rectangular park are:

- Length = 58 yards
- Width = 33 yards

Using the Pythagorean theorem:

\[
d = \sqrt{(length^2 + width^2)}
\]

Substituting the given values:

\[
d = \sqrt{(58^2 + 33^2)}
\]

Calculating the squares:

\[
58^2 = 3364
\]
\[
33^2 = 1089
\]

Now sum these two values:

\[
3364 + 1089 = 4453
\]

Taking the square root:

\[
d = \sqrt{4453} \approx 66.7
\]

Rounding to the nearest tenth, the length of the diagonal path is approximately:

\[
\boxed{66.7} \text{ yards}
\]