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.
Answers
GPT-4o mini
To find the length of the diagonal path in the rectangular park, we can use the Pythagorean theorem. The formula for the length of the diagonal \(d\) in a rectangle is given by:
\[
d = \sqrt{l^2 + w^2}
\]
where \(l\) is the length and \(w\) is the width of the rectangle.
In this case, the dimensions of the park are:
- Length \(l = 494949\) yards
- Width \(w = 424242\) yards
Now, we can calculate the diagonal:
\[
d = \sqrt{(494949)^2 + (424242)^2}
\]
First, let's calculate \( (494949)^2 \) and \( (424242)^2 \):
\[
(494949)^2 = 244927755060801
\]
\[
(424242)^2 = 179999622976964
\]
Now, add these two results together:
\[
(494949)^2 + (424242)^2 = 244927755060801 + 179999622976964 = 424927378037765
\]
Now we take the square root:
\[
d = \sqrt{424927378037765} \approx 651441.4
\]
Rounding to the nearest tenth, the length of the diagonal path will be:
\[
\boxed{651441.4} \text{ yards}
\]
\[
d = \sqrt{l^2 + w^2}
\]
where \(l\) is the length and \(w\) is the width of the rectangle.
In this case, the dimensions of the park are:
- Length \(l = 494949\) yards
- Width \(w = 424242\) yards
Now, we can calculate the diagonal:
\[
d = \sqrt{(494949)^2 + (424242)^2}
\]
First, let's calculate \( (494949)^2 \) and \( (424242)^2 \):
\[
(494949)^2 = 244927755060801
\]
\[
(424242)^2 = 179999622976964
\]
Now, add these two results together:
\[
(494949)^2 + (424242)^2 = 244927755060801 + 179999622976964 = 424927378037765
\]
Now we take the square root:
\[
d = \sqrt{424927378037765} \approx 651441.4
\]
Rounding to the nearest tenth, the length of the diagonal path will be:
\[
\boxed{651441.4} \text{ yards}
\]