Question

a rectangle park is 14 miles long and 7 miles wide how long is a pedestrian rout that runs diagonally across the park

Answer 1

15.65 miles

Explanation:

The diagonal of a rectangle is basically a divider for two triangles whose areas are the same inside the rectangle.

Using Pythagorean Theorem to find the hypotenuse (the longest side aka the diagonal) - this can be written in two ways:

`a^(2) + b^(2) = c^(2)`

or

c =
`√(a^2 + b^2)`

Let's use
`√(a^2 + b^2)`.

"A" represents one side length/leg, "B" represents the other side length/leg, and "C" represents the hypotenuse/the longest side (aka the diagonal in this case).

We are given two side lengths (legs):

A = 14 miles long

B = 7 miles wide

Plug it into the formula;

c =
`√(a^2 + b^2)`

c =
`√(14^2 + 7^2)`

c =
`√(196 + 49)`

c =
`√(245)`

C = 15.6524758425

Let's round to the nearest hundredth:

C = 15.65 miles is the hypotenuse.