Let's elaborate it
As the question reads "12 M North" then "12 M East" and then "12 M North"
It equals to North=12+12 (24)
East=(12)
Let's suppose the man goes 12 M East first and then 24 M North.
As he goes "straight" we have two lines with an angle of 90.
Now we have three points A,B and C.
Point
A is the Home, the starting point.
Point
B 12 M Eastwards from point A.
Point
C 24 M Northwards from point B.
We have been told that the man has taken a straight course to home(point
A) from "point
C"
Thus we got a third line drawn from C to A.
What we get as a result is a Triangle. A
right triangle (a triangle with one
right angle which measures to 90 degrees).
We have to measure the length the man covered in his return journey.
what we need is to measure the length of our third line (A to C)
That is simply the
Hypotenuse and we could measure its length by using
Pythagorean theorem which states that which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides of a right triangular.
h square=12 square+24 square
h square=144+576
h square=720
take square root on both sides of equation
h=26.83
Now we have the exact lengths
If you want the total time elapsed and have the speed just measure it on basis of these lengths.