If 5 points are chosen in a square of side 2cm, show that there will always be two points at a distance of at most √ 2cm.
The Answer to the Question
is below this banner.
Can't find a solution anywhere?
NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?
Get the Answers Now!You will get a detailed answer to your question or assignment in the shortest time possible.
Here's the Solution to this Question
We bisect the square in 4 equal parts.
So by pigeonhole principle 1 portion contains atleast two points.
Now the length of the sides of each square becomes 1 cm.
So the maximum distance between two points in a square (newly formed) is the length of the
diagonal= .
Hence in the square portion which contains 2 points are at a distance atmost cm.