meenakshibehera wrote:
but here the question asks for rectangles . I think this no 150 includes even squares also . like vertical grid line 2and 4 will give a square in combination with horizontal lines( 1,3) ; (2,4) ; (3,5) and so on should we not exclude them from this no .
You are right.
The solution presented includes square as well. The formulae is blindly applied to include squares.
To prove,
we can solve a simple combination.
Let's take a 2X3 rectangle grid made up of small squares. Applying the same logic, it will be 3C2 X 4C2 = 3*6 = 18. This will include squares as well.
There are only 10 such rectangles which can be formed here.
rectangles with 1x2 = 2 per row = 4 in total
rectangles with 2x1 = 1 per column = 3 in total
rectangles with 1x3 = 1 per row = 2 in total
rectangle with 2x3 = 1 in total
Moreover, there are 8 such squares in total
squares 1x1 = 2*3 = 6
squares 2x2 = 1*2 = 2
Now, applying the same to the question.Total quadrilaterals that can be formed is 5C2 * 6C2 = 10*15 = 150.
The number of squares in this will include = 4*5 + 3*4 + 2*3 + 1*2 = 40
Hence, the total number of rectangles will be 150 - 40 = 110With respect to the question, I suppose (looking at the picture), the smaller units appear to be rectangle. Hence, the question was incorrectly worded as 20 equal squares instead of 20 equal rectangles. If it is the latter, 150 is right.