There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that 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?
Explanation:
There are 5 parallel lines and there are another 'n' lines which are parallel but perpendicular to the first 5 lines.
∴ Each of the first 5 lines (say they are all horizontal lines) are perpendicular to each of the other n lines (say they are vertical lines).
To form a rectangle we need two horizontal and two vertical lines.
∴ Number of rectanges = (number of ways of selecting 2 horizontal lines) × (number of ways of selecting 2 vertical lines)
⇒ 360 = 5C2 × nC2
⇒ 360 = 10 × n(n - 1)/2
⇒ 72 = n(n - 1)
⇒ n = 9
Hence, 9.
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