Question

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

Answer 1

To create a rectangle or a square you need to SELECT 2 of the vertical lines and 2 horizonal lines.
Hence answer is
4C2 × 4C2 , where 'C' is combination.
= 6 × 6
= 36
Hence answer is
☆》36

Answer 2

Solution :-

The number of rectangles or squares that can be formed by using 'm'

horizontal lines and 'n' vertical lines are = mс₂ × nс₂

Here m = 4 and n = 4

Hence, the number of rectangles or squares that can be formed

= mc₂ × nc₂

= 4c₂ × 4c₂

= (4c₂)²

= [(4*3)/(2*1)]²

= (12/2)²

= 6²

= 36

Hence, maximum 36 rectangles or squares can be formed.

Answer.