a rectangle park is 14 miles long and 7 miles wide how long is a pedestrian rout that runs diagonally across the park
To find the length of the pedestrian route that runs diagonally across the rectangle park, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two other sides of the right-angled triangle are the length and the width of the park. Let's call the length L and the width W.
Therefore, L = 14 miles and W = 7 miles.
Using the Pythagorean theorem, the length of the diagonal (D) can be calculated as:
D^2 = L^2 + W^2
D^2 = 14^2 + 7^2
D^2 = 196 + 49
D^2 = 245
Taking the square root of both sides, we find:
D = √245
D ≈ 15.652 miles
Therefore, the length of the pedestrian route that runs diagonally across the park is approximately 15.652 miles.
To find the length of the pedestrian route that runs diagonally across the rectangle park, you can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the rectangle are the two sides of the triangle, and the diagonal is the hypotenuse. Let's denote the length of the rectangle as 'l' and the width as 'w'.
We can now calculate the diagonal as follows:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 14^2 + 7^2
Diagonal^2 = 196 + 49
Diagonal^2 = 245
To find the length of the diagonal, we can take the square root of both sides:
Diagonal = sqrt(245)
Therefore, the length of the pedestrian route that runs diagonally across the park is approximately 15.65 miles.