A set of 10 parallel lines is intersected by | vedclass

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Question

(D) parallelogram is formed by selecting $2$ lines from the first set of $10$ parallel lines and $2$ lines from the second set of $m$ parallel lines.

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) parallelogram is formed by selecting $2$ lines from the first set of $10$ parallel lines and $2$ lines from the second set of $m$ parallel lines. The number of ways to choose $2$ lines from $10$ is given by ${}^{10}C_2 = \frac{10 	imes 9}{2} = 45$. The number of ways to choose $2$ lines from $m$ is given by ${}^{m}C_2 = \frac{m(m-1)}{2}$. The total number of parallelograms is the product of these two combinations: ${}^{10}C_2 	imes {}^{m}C_2 = 675$ $45 	imes \frac{m(m-1)}{2} = 675$ $\frac{m(m-1)}{2} = \frac{675}{45} = 15$ $m(m-1) = 30$ $m^2 - m - 30 = 0$ $(m - 6)(m + 5) = 0$ Since $m$ must be positive,$m = 6$.

$A$ 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:

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