how many squares and rectangle has in chase board ??prove your answer...

• a chess board has 9 vertical & 9 horizontal lines
  no. of square of size 1*1=8*8=8^2
  no. of square of size 2*2=7*7=7^2
  no. of square of size 3*3=6*6=6^2
  ........
  similarly
  no of square of size 8*8=1*1
  so total no. of square=
  1^2+2^2+3^3+...+8^2=8(8+1)(2*8+1)/6=204
  
  a chess board has 9*9 lines
  to form a rectangle
  we have to choose 2 of the 9 vertical lines and 2 of the 9 horizontal lines
  as square is also a rectangle
  so no. of rectangles=9C2*9C2=36*36=1296
  
  
• 10 years agoHelpfull: Yes(4) No(1)
• for sqre u do , 1^2+2^2+3^2.....+8^2 , that is 17*12 squares
  for recatangles u do 1^3+2^3+3^3+....+8^3, that is 36*36 rectangles =1296
• 10 years agoHelpfull: Yes(2) No(0)
• No'of squares equal to 'the sum of the squares of the first n natural numbers i.e
  n(n+1)(2n+1)/6.
  so here n=8 because it has 8 horizontal and 8 vertical lines.
  now ANS= 8(9)(17)/6=204.
• 10 years agoHelpfull: Yes(0) No(0)
• No. of square= sigma of x*x = n*(n+1)*(2n+1)/6=204
  
  No. of rectangle = sigma of x*x*x =[n*(n+1)/2]*[n*(n+1)/2] =1296
• 10 years agoHelpfull: Yes(0) No(0)
• [n(n+1)/2]^2-----for total rectangle = 1296
  
• 10 years agoHelpfull: Yes(0) No(0)
• [RAJRATAN]
  [n(n+1)/2]^2-----for total rectangle = 1296
  [n*(n+1)(2n+1)]/6-----for square = 204
• 10 years agoHelpfull: Yes(0) No(0)
• no.of squares = n(n+1)(2n+1) /6=204
  no.of rectangles=(n+1)c2 * (n+1)c2=1296
  as n=8.....
• 9 years agoHelpfull: Yes(0) No(0)