Question
A rectangular park that measures 797979 yards by 777777 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.
Answers
GPT-4o mini
To find the length of the diagonal path in a rectangular park, we can use the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle is given by:
\[
d = \sqrt{l^2 + w^2}
\]
where \( l \) is the length and \( w \) is the width. In this case, we have:
- Length \( l = 797979 \) yards
- Width \( w = 777777 \) yards
Now, we can calculate the diagonal:
\[
d = \sqrt{(797979)^2 + (777777)^2}
\]
Calculating \( (797979)^2 \):
\[
(797979)^2 = 635198456084441
\]
Calculating \( (777777)^2 \):
\[
(777777)^2 = 604444456929729
\]
Now we add these two results:
\[
(797979)^2 + (777777)^2 = 635198456084441 + 604444456929729 = 1230642910141170
\]
Taking the square root to find the length of the diagonal:
\[
d = \sqrt{1230642910141170} \approx 1109.538...
\]
Rounding this to the nearest tenth gives:
\[
d \approx 1109.5
\]
Thus, the length of the diagonal path will be approximately **1109.5 yards**.
\[
d = \sqrt{l^2 + w^2}
\]
where \( l \) is the length and \( w \) is the width. In this case, we have:
- Length \( l = 797979 \) yards
- Width \( w = 777777 \) yards
Now, we can calculate the diagonal:
\[
d = \sqrt{(797979)^2 + (777777)^2}
\]
Calculating \( (797979)^2 \):
\[
(797979)^2 = 635198456084441
\]
Calculating \( (777777)^2 \):
\[
(777777)^2 = 604444456929729
\]
Now we add these two results:
\[
(797979)^2 + (777777)^2 = 635198456084441 + 604444456929729 = 1230642910141170
\]
Taking the square root to find the length of the diagonal:
\[
d = \sqrt{1230642910141170} \approx 1109.538...
\]
Rounding this to the nearest tenth gives:
\[
d \approx 1109.5
\]
Thus, the length of the diagonal path will be approximately **1109.5 yards**.