From a point P, R is 5km due west and 12km due south. Find the distance between P and R

To find the distance between points P and R, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we can consider P, R, and the point where the southward line from P intersects with the westward line from R, forming a right-angled triangle as shown in the diagram below:

                   R
                   *
                   |
                   |
                   |12 km
                   |
                   |
            *------P
          5 km

Let's call the point where the two lines intersect Q. Then we can see that the distance between P and Q is 5km, and the distance between Q and R is 12km. Therefore, we can use the Pythagorean theorem to find the distance between P and R as follows:

distance between P and R = sqrt(5^2 + 12^2)
                         = sqrt(169)
                         = 13 km

Therefore, the correct answer is 13km.