Question

A rectangular park that measures 494949 yards by 424242 yards will have a diagonal path built. How long will the path be? Round your answer to the nearest tenth. Click Here for Help Video.

Answer 1

To find the length of the diagonal path in a rectangular park, you can use the Pythagorean theorem. The formula is given by:

\[
d = \sqrt{a^2 + b^2}
\]

where \( d \) is the length of the diagonal, \( a \) is the length of one side, and \( b \) is the length of the other side.

Given:
- Length \( a = 494949 \) yards
- Width \( b = 424242 \) yards

Now, substituting the values into the formula:

\[
d = \sqrt{(494949)^2 + (424242)^2}
\]

Calculating \( (494949)^2 \):

\[
(494949)^2 = 244930079760001
\]

Calculating \( (424242)^2 \):

\[
(424242)^2 = 180150575056964
\]

Now add the two results:

\[
244930079760001 + 180150575056964 = 425080654816965
\]

Now, take the square root:

\[
d = \sqrt{425080654816965} \approx 651070.7534
\]

Rounding to the nearest tenth:

\[
d \approx 651070.8
\]

Thus, the length of the diagonal path is approximately **651070.8 yards**.