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

To solve this, you must know what the Pythagorean Theorem is. 
Here's a crash course: any length of a side (a) squared plus the other side of a triangle (b) squared is equal to the long side (c) squared. This also works if you're trying to find the length of the diagonal of a square. 

So, if Mara ran 3 km north then 4 km east, you would come out with the equation:

3^2+4^2=c^2

Solve using order of operations. 

3^2+4^2=c^2
9+16=c^2
25=c^2
5=c

This is the length of the run directly home. To get the total distance run, just add up all the sides of her triangle-shaped run. 

3+4+5=12

She ran 12 km. 

Hope this helps!