If the number of rectangles formed on a chess board is 1296, then the total number of squares formed on the chess board is

Step-by-step solution

It is given that the number of rectangles formed in chess board (Let having size (n n )) is 1296 ( aligned & ^ n+1 C₂ ^ n+1 C₂=1296 & ( n(n+1) 2 )^2=1296=(36)^2 & n(n+1) 2 =36 n(n+1)=72 n=8 aligned ) So, number of squares of any sizes are ( aligned & n^2+(n-1)^2+(n-2)^2+ .+1^2 & =1^2+2^2+3^2+ +8^2 & = 8 9 17 6 =4 3 17=12 17=204 aligned ) Hence, option (c) is correct.