A rectangle has 90 degree angles. When a line cuts it diagonally, it makes a right angle. (I drew the picture on a rocking chair so...)
When there is a right angle we think about the Pythogarean theorem.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Plug the values:
[tex] {8}^{2} + {6}^{2} = {x}^{2} [/tex]
Simplify:
[tex]64 + 36 = {x}^{2} [/tex]
Combine like terms:
[tex]100 = {x}^{2} [/tex]
Take the square root of both sides:
[tex]10 = x[/tex]
The length of the path is 10 miles.
