A set of 10 parallel lines is intersected by another set of m parallel lines. If the total number of parallelograms formed by these two sets of lines is 675 . Then m is equal to

Step-by-step solution

Given, 10 parallel lines and m parallel lines since one parallelogram can be formed by the intersection on one pair of parallel lines with another pair of another set of parallel lines. Number of parallelograms = ¹⁰ C₂ ^m C₂ 675= 10 9 2 m(m-1) 2 30=m(m-1) m^2-m-30=0 (m-6)(m+5)=0 m=6