Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How far apart are Jacob and Sharon now?
Responses
A 5 m
B 8 m
C 13 m
D 18 m
E 24 m
B 8 m
To find the distance between Jacob and Sharon, we can use the Pythagorean theorem.
The distance from Jacob's final location to the starting point is the hypotenuse of a right triangle with legs of length 3 m and 4 m. Using the theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
c = 5 m
Similarly, the distance from Sharon's final location to the starting point is the hypotenuse of a right triangle with legs of length 5 m and 12 m. Using the theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 5^2 + 12^2
c^2 = 25 + 144
c^2 = 169
c = 13 m
Therefore, the distance between Jacob and Sharon is 5 m + 13 m = 8 m.