Pythagorean theorem: a rectangular park is 6 miles long and 5 miles wide. how long is a pedestrian route that runs diagonally across the park?

explain/show steps

The exact length is sqrt(61) miles which approximates to 7.8102 miles

================================================

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