+1 vote
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number of rectangles in a chess board that are not sqaure

a)1296

b)1092

c)1096

d)1292
| 141 views
0
b) 1092
0
how?

in the chessboard, There are 9 horizontal lines and 9 vertical lines. Choose two distinct horizontal lines, and two distinct vertical lines.  (any rectangle determines a pair of horizontal lines and a pair of vertical lines)

so # rectangle = 9C2 * 9C2  = 1296

u can see that there are 82 small 1×1  squares, 72   2×2 squares, and so on down to 12     1×1 squares,,, u need to add to find total # squres

so # squres = 1+ 22 + 32 + 4+ 5+ 6+ 7+ 82  =  204

number of rectangles in a chess board that are not sqaure = 1296 - 204 = 1092

by Boss (12.2k points)
selected by
0
Very well, great job.
+1 vote

Explanation:-

No of Squares :-

 Dimension No of Squares 1X1 64 2X2 49 3X3 36 4X4 25 5X5 16 6X6 9 7X7 4 8X8 1

So no of squares = 204

No of Rectangles :-

In chess board we have 9 vertical lines and 9 horizontal line, now to construct rectangle of any dimension we have to take 2 horizontal line and 2 vetical line, which can be done in

= C(9,2) * C(9,2)

= 36 * 36

= 1296

To get total no of Rectangles which are not square simply subtract total no of squares from total no of rectangle.

= Total no of rectangles - total no of squares

= 1296 - 204

= 1092

by Boss (18.2k points)