Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the
triangle did. The initial number of balls is

• 1540balls initially there.
  
  n(n + 1)/2 + 669 = (n - 8)^2
  
  => n^2 - 33n - 1210 = 0
  => (n - 55)(n + 22) = 0
  => n = 55
  
  => n(n + 1)/2 = (55* 56)/2 = 55 * 28 = 11 * 140 = 1540
• 12 years agoHelpfull: Yes(7) No(1)
• Answer 1540
  
  suppose there n rows in equilateral triangle .then no.of balls=n(n+1)/2
  
  now 669 more balls are added and forms a square with sides of n-8 balls.
  
  therefore 669+n(n+1/2=(n-8)²
  
  simplifying we get n²-33n-1210=0
  
  n=55
  
  therefore no.of balls = 55*56/2=1540
  
  actually we are finding a triangular no. which is 669 less than a perfect square.(1540+669=2209,which is a perfect square)
  
• 12 years agoHelpfull: Yes(3) No(0)