Q. 325.0( 2 Votes )

A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.

Answer :

We know that parallelogram has 4 lines in which 2 sides are parallel to each other which means 2 pairs of lines are parallel lines


It is told that parallelogram is cut by two sets of m lines parallel to its sides.


This means there will be two sets of (m + 2) lines parallel to each other.


We need two sets of parallel lines to form a parallelogram in which the lines need to be chosen from these two sets of (m + 2) parallel lines.


Let us assume that the no. of parallelograms formed be N.


N = (choosing 2 parallel lines from (m + 2) parallel lines which are parallel to one side) × (choosing 2 parallel lines from (m + 2) parallel lines which are parallel to the side which is not parallel to the first side)


N = (m + 2C2) × (m + 2C2)


N = (m + 2C2)2


We know that ,


And also n! = (n)(n – 1)......2.1






The total no. of parallelograms formed are .


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