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# a parallelogram is cut by two sets of m parallel lines to its sides. find the no. of parallelograms formed..

147 Points
11 years ago

Dear ajinkya

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

then we have  2 sets of (m+2) parallel lines ( 2 lines of the parallelogram)

so parallelogram is formed by taking 2 lines from each set

= m+2C2 * m+2C2

= [(m+2)(m+1)/2 ]2

this also include 1 original parallelogram

so total number of new parallelogram formed is  =   [(m+2)(m+1)/2 ]2   -1

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Neerav
15 Points
3 years ago
a and b sides of pgm is used as border. hence, 2 sides remain.- PART 1
if x given is more than exact amount, take x as x+1-PART 2
but here, we have 2 sides, i.e. x+2.-PART 3
SINCE WE HAVE 2 SETS, C(M+2,2)*C(M+2,2)