The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:

Question

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines: (A) 6 (B) 9 (C) 18 (D) 12

Tardigrade Admin · Accepted Answer

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms

=^{m} C_{2} \times^{n} C_{2} = \frac{mn ( m - 1 ) ( n - 1 )}{4}

In given ques, m = 4, n = 3

∴

Number of parallelogram formed

= \frac{12 ( 3 ) ( 2 )}{4} = 18

Q. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:

6

9

18

12

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms =mC2​×nC2​=4mn(m−1)(n−1)​ In given ques, m = 4, n = 3 ∴ Number of parallelogram formed =412(3)(2)​=18

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms
$=^{m} C_{2} \times^{n} C_{2} = \frac{mn ( m - 1 ) ( n - 1 )}{4}$
In given ques, m = 4, n = 3
$∴$ Number of parallelogram formed
$= \frac{12 ( 3 ) ( 2 )}{4} = 18$