IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 4 : 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?

Video Explanation

Explanatory Answer

A rectangle essentially is two mutually parallel lines and another pair of mutually parallel lines perpendicular to them.
We have 5 parallel lines in a plane, let us assume the number of lines that are perpendicular to these lines is ‘n’.
To make a rectangle we need 2 lines from each group. This can be done in ⁵C₂ * ⁿC₂ ways.
So from the groups having 5 and n lines. we get ⁵C₂ * ⁿC₂ rectangles.
Therefore, ⁵C₂ * ⁿC₂ = 360
On solving we get 10 * \(\frac{n(n-1)}{2}\) = 360
=> n(n-1) = 72
=> n = 9

The answer is '9'

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