this morning (just before going to school), Calvin and Klein decided to race and see who will be choosing the shortest rout to reach the school first .
hey Klein, would you want to race with me and see who will reach the school first?
- Me, I think I will start by going through the north- Let's start the game.
- OK sure, but if you lose you have to admit that I am smarter than you.- I am starting towards the north east , what about you?
Legend:- the thin blue arrow is Calvin's path.- the thick orange arrow is Klein's path.
Wow Klein! How did you reach this fast? Moreover, I did not see you go through the same path that I chose!
- Wait, I covered 23 Km. Can you explain to me the math that you did to get the answer ? Because I am impressed!
- As I told you before, I went towards the north east. I used some math and calculated my distance that is equal to 16.95 Km.
- Yah sure...
1) At first I used some reasoning to make sure of my calculations such as:- angle H = angle C ( alternating angles)- angle AXH = angle BXC ( vertical angles)- angle A = angle B ( alternating angle / right angle)thus my conclusion was that both triangles are right angled 2) Now I made sure that both triangles are similar, I used the ratios of corresponding side as they were equal to find certain variables:- = - x = 5.6 Km ( x is the distance from X to B)3) Then I used Pythagoras theorem to find the rest:- the side HX = 10.6 Km- the side CX = 6.35 4)
10.6 6.35 16.95 Km
15 -X X
Wow Klein! You impressed me, I admit that you are smarter than me.
- Now since we are done let's go our classes before the bell rings