A rectangular park is 6 miles long and 3 miles wide. How long is a pedestrian route that runs diagonally across the park?

As it will create a triangle with 90o angle the pythagory says 6+3²=x²⇔ x²=45⇔ x=√45

If the path runs diagonally, then a right angle triangle is made, with the width and length as the two sides, and the route taken as the hypotenuse.

Pythagorus' Theorem tells us that; A² = B² + C²

Where B and C are the two sides of a right angled triangle, and A is the hypotenuse.

Route taken = A

A² = B² + C²

A² = 3² + 6²

A² = 9 + 36

A² = 45

A = √45

A = 6.7 miles