Answer:
The route across the park is 40 meter shorter than the route around its edges.
Step-by-step explanation:
We have to calculate the distance for both routes
As the route around the edges is straight, we have to find the sum of length of both edges
Let [tex]R_E[/tex] be the distance of route around edges
[tex]R_E = 80+60 = 140\ meters[/tex]
Now we know that a diagonal divides a rectangle in two right angled triangles in which the diagonal is the hypotenuse.
We can use Pythagoras theorem to find the length of the diagonal
So,
[tex]H^2 = P^2 + B^2[/tex]
In the given scenario
P = 60
B = 80
Now
[tex]H^2 = (60)^2 + (80)^2\\H^2 = 3600+6400\\H^2 = 10000\\\sqrt{H^2} = \sqrt{10000}\\H = 100\ meters[/tex]
In order to calculate that how much shorter is the path across the park, we have to subtract the distance across park from the distance across edges.
[tex]= 140-100 = 40\ meters[/tex]
Hence,
The route across the park is 40 meter shorter than the route around its edges.
