Question
Sat June 30, 2012 By:
 

How many squares can be formed b/w m parallel horizontal lines & n parallel vertical lines.

Expert Reply
Sun July 01, 2012
Answer :Given : m parallel horizontal lines , and n parallel vertical lines.
to find : the no. of squares formed by these given lines.
 
Since we know a single square can be formed using 2 parallel horizontal lines and 2 parallel vertical lines. since the lines are parallel and one is horizontal, other is vertical, it would satisfy all the properties of a square to be formed i.e each angle on vertice is 90 degree with all sides equal .
 
As we know , if there are 4 horizontal lines , then 3 blocks are made 
                      |    1      |    2       |    3     |
 
similarly  , if there are 3 vertical lines , 2 blocks willbe formed
--------
1
--------
2
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=> if they are combined = 3*2 = 6 blocks would be formed
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      |                     |                       |                         |
      |                     |                       |                         |
      |      1             |          2           |         3              |
----------------------------------------------------------------------------
      |                     |                        |                         |  
      |      4             |          5            |        6               |
      |                     |                        |                         |  
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therefore if we see this same problem in the same note , we see that (m-1) * (n-1) total sqares will be formed. 
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