Question

There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed? 

(a) 16 

(b) 24 

(c) 36

(d) 42

Answer 1

Correct option (c) 36

Explanation:

The board will be a 3 × 3 one and will look as follows:

We know that to form a square/rectangle we need 2 horizontal and 2 vertical lines.

The number of ways in which 2 vertical lines may be chosen from 4 = ⁴C² = (4 × 3)/2 = 6

Similarly, number of ways in which 2 horizontal lines may be chosen from 4 = ⁴C² = (4 × 3)/2 = 6

Hence, the maximum number of squares and rectangles that can be formed = 6 × 6 = 36