saswata4s wrote:

The figure below shows a rectangle ABCD in the xy- coordinate plane. The sides AB and AD are parallel to the x- and the y- axis respectively. How many squares of side 1 unit that lie on or inside the rectangle ABCD can be drawn?

(1) The length of side AB is 6 units

(2) The coordinates of points A and C are (3,2) and (9, 5)

I personally think that the question

should mention 'How many squares of side 1 unit and

with all its vertices having integer coordinates' that lie on or inside the rectangle ABCD can be drawn.

That is because if we do not mention that the vertices of square have to be integers, then actually infinite squares can be made.

Eg, we start with the first square of side 1 unit which is at the leftmost bottom position in this rectangle, i.e., the square whose bottom left vertex is A. Now if we assume the coordinates of A to be (3,2) then the other three vertices will be at (4,2); (4,3) and (3,3).

Now if we just shift this square by 0.1 units on the right, then we will have another different square with side 1 unit having the four vertices as: (3.1,2); (4.1,2); (4.1,3) and (3.1,3).

Similarly we can shift that first square 0.1 units up (instead of right) and we will have another square. Similarly, instead of shifting 0.1 units we could also shift by 0.01 units or 0.02 units. So we can just make the first square anywhere in this rectangle and then keep shifting it very slightly to right/left and/or top/bottom - thereby resulting in infinite squares.