Answer: The exact length is sqrt(61) miles which approximates to 7.8102 miles
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Work Shown:
See the attached image below. Draw a rectangle that is 6 by 5. Then add a diagonal line to represent the pedestrian route. This forms a right triangle. The right triangle has legs of 6 and 5. The hypotenuse is unknown, which we'll call x.
a = 6
b = 5
c = x
Use the pythagorean theorem to solve for x
a^2 + b^2 = c^2
6^2 + 5^2 = x^2
36 + 25 = x^2
61 = x^2
x^2 = 61
x = sqrt(61) which is the exact length
x = 7.8102 which is the approximate length
