carmen walked 30 yards due north and 12 yards west, but then she went directly back to her starting point, as shown by the dotted line. how far (to the nearest yard) did carmen travel to get back to where she started?

a 42 yards

b 32 yards

c 21 yards

d 21 yards

32 yards

Step-by-step explanation:

Carmen walked 30 yards due North and 12 yards West.

Now, if we join the initial and final position of Carmen and in this path Carmen comes back to her original position then the path, traveled by Carmen will form a right triangle and the direct path from her initial point to final point will be the hypotenuse of the right triangle.

Now, the two perpendicular legs of the triangle are respectively 30 yards and 12 yards.

Therefore, Carmen travel (Applying Pythagoras Theorem) to get back to her initial position by yards ≈ 32 yards (to the nearest yard). (Answer)