A Square of side 5 cm .the midpoints are joined to form a smaller square.this process is repeated.What will be the perimeter of 9th square?

• 2nd inner sq:side=5/sqrt2*1
  3rd inner sq:side=5/sqrt2*2
  4th inner sq:side=5/sqrt2*3
  ..
  ..
  ..
  9th inner sq:side=5/sqrt2*8
  =5/4 ans
• 11 years agoHelpfull: Yes(1) No(0)
• area of square = a^2;
  1). area of square after joining midpoints = (a^2)/2;
  2). area of square after joining midpoints of square constructed in step 1=((a^2)/2)/2 i.e (a^2)/4.
  hence in 9th step area of square would be (a^2)/2^9=(a^2)/512.
  and perimeter will be 4*sqrt((a^2)/512).
• 11 years agoHelpfull: Yes(0) No(1)