Suppose you travel north for 65 kilometers then travel east

Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point?

Solution

Start from a point A
Go vertically up to a point B
Mark this length AB = 65
Go horizontal from B to a point C with length BC slightly longer than AB.
Mark this length BC= 75
You started your journey at A. Went up north to B. Went east from B to C.
If now you join A and C, then the length CA gives the distance from your destination C to the starting point A.
If you look at your diagram, it is a right angled triangle with
angle B = 90 degrees. AC is the hypotenuse.
So by Pythog. theorem
AC^2 = AB^2 + BC^2
=(65)^2 + (75)^2
= 4225 +5625
=9850
Then AC = sqrt(9850)which is approximately 99.25 kilometers
Answer: The required distance is approximately 99.25 kilometers