Answer:
miles
This is the same as writing 6*sqrt(5) miles
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Work Shown:
P = park
C = city hall
Point P is at the location (10,11)
Point C is at the location (7,5)
Apply the distance formula to find the length of segment PC
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%2810-7%29%5E2%20%2B%20%2811-5%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%283%29%5E2%20%2B%20%286%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B9%20%2B%2036%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B45%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B9%2A5%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B9%7D%2A%5Csqrt%7B5%7D%5C%5C%5C%5Cd%20%3D%203%5Csqrt%7B5%7D%5C%5C%5C%5Cd%20%5Capprox%206.7082039%5C%5C%5C%5C)
The exact distance between the park (P) and city hall (C) is
miles.
This doubles to
miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.
Extra info:
so the runner travels a total distance of roughly 13.4 miles.