Mara ran 3km north and then 4km east. She will finish her run by running directly home. What was the total distance of her run?

So we need to find the length of the hypotenuse of a right triangle with sides of 3 and 4, then add that distance to 3 and 4.

By the Pythagorean Theorme, the hypotenuse squared is equal to the sum of the sides squared ...

d^2=3^2+4^2

d^2=9+16

d^2=25

d=√25

d=5

So the total distance of her run is 5+4+3=12 km