There are 5 parallel lines on the plane. On the same plane, there are n other lines which are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of n?

There are five parallel lines, and n lines that are perpendicular to them. To form a rectangle, we need two lines that are parallel and two lines that are perpendicular to the two parallel lines. Thus, we need to choose 2 lines from the 5 parallel lines, and 2 lines from the n lines which are perpendicular to them.

Total number of rectangles = $$^5C_2\times\ ^nC_2$$

In the question, we are given the total number of rectangles as 360.

=> $$^5C_2\times\ ^nC_2=360$$

=>$$10\times\ ^nC_2=360$$

=>$$^nC_2=36$$

=> $$n=9$$