A square of side x is given... joining the mid point of the sides another square is made...in this way it is continued...what will be the perimeter of the the 9th square???

• area of 1st square = x^2
  area of 2nd square = x^2/2 = x^2/2^1
  area of 3rd square = x^/4 = x^2/2^2
  area of 4th square = x^2/8 = x^2/2^3
  ......
  
  area of 9th square = x^2/2^8
  
  perimeter of 9th square = 4*side = 4* √(x^2/2^8) = 4*x/2^4 = 4*x/16 = x/4
  
  
• 10 years agoHelpfull: Yes(53) No(8)
• area of 1st square = x^2
  area of 2nd square = x^2/2 = x^2/2^1
  area of 3rd square = x^/4 = x^2/2^2
  area of 4th square = x^2/8 = x^2/2^3
  ......
  
  area of 9th square = x^2/2^8
  
  perimeter of 9th square = 4* √(x^2/2^8) = 4*(x/2)^4 = 4*x/16 = x/4
• 10 years agoHelpfull: Yes(7) No(0)
• since 2nd square made by joining the mid points of 1st square results sides = x/2sqrt(2)..similarly 3rd square have side x/2..then 5th as x/4..7th as..x/8..and 9th square as x/16.
  Hence perimeter of 9th square is 4*x/16 = x/4 ans
• 10 years agoHelpfull: Yes(3) No(2)
• Area of a square joining the midpoints of another square is half the area of original square.
  ie area of 2nd square = x^2/2
  area of nth square = x^2/2^(n-1)
  similarly area of 9th square = x^2/2^8
  = x^2/256
  ====> side of 9th square = x/16
  perimeter = 4*side = 4*x/16 = x/4
  
• 10 years agoHelpfull: Yes(3) No(0)
• p1- 4a (side be a the perimeter = a+a+a+a =4a)
  p2- 2a (side be a the perimeter = a/2+a/2+a/2+a/2 =2a) so on..
  p3- a
  p4- a/2
  p5- a/4
  p6- a/8
  p7- a/16
  p8- a/32
  p9- a/64
• 10 years agoHelpfull: Yes(3) No(7)
• in the qtn the side was 5 cm.
  1st square-----------> 5 cm
  2nd square----------->5/root(2)
  3rd square-----------> 5/root(2)*root(2)
  .
  .
  so on.
  n times---- 5/(root(2))^n-1
  here n=9
  so 9th square's side will be 5/root(2)^8=5/16
  perimeter=4*5/16=5/4
  
• 10 years agoHelpfull: Yes(2) No(0)
• 1 sq side = x
  2 sq side = x/2
  3 sq side = x/4
  Similarly 9th sq side = x/(2^8)
  
  So perimeter is 4*x/(2^8)= x/64
• 10 years agoHelpfull: Yes(2) No(2)
• If x is the side of the outer Square then its Perimeter will be 4x
  Now ,another square is made using the mid points off all the four sides
  then each side of the inner Square will be x/sqrt(2).
  
  Therefore its Perimeter will be 8*sqrt(2)*x
  
  Similiarly, 3rd Square will have Perimeter 2x
  4th will have 4*sqrt(2)*x
  .
  .
  .
  .
  9th Square will have Perimeter x/4
• 10 years agoHelpfull: Yes(1) No(0)
• Answer: x/4sqrt(2)
  
  Since a square is made by joining the mid points, therefore diagonal of the new square thus formed is equal to the side of the mother square(draw the fig to understand). Since, a diagonal is given by length*sqrt(2)and length is "x", diagonal of the new square is "x".
  let the length of each side of new square be a1
  then, a1=x/sqrt(2)
  Again, a2=x/2
  a3=x/2sqrt(2)
  a4=x/4
  .
  .
  .
  a9=x/16sqrt(2)
  Thus, each side of 9th square is x/16sqrt(2)
  
  Now, perimeter of 9th square is x/4sqrt(2)
  
  Thank you.
• 10 years agoHelpfull: Yes(1) No(4)
• all are doing
  perimeter =4*area
  its 4*side i think...
• 10 years agoHelpfull: Yes(1) No(1)
• x/4 is the ans
  
• 10 years agoHelpfull: Yes(0) No(2)
• komal and rohit are true .. i think.
• 10 years agoHelpfull: Yes(0) No(2)
• it is given that the square is side of x
  so side of 1st sqr= x
  2nd= x/2
  3rd= x/4
  ...
  
  9th x/256
  so side of 9th square is x/256
  hence perimeter is= 4*x/256= x/64 ....
• 10 years agoHelpfull: Yes(0) No(1)
• x/64
  becoz perimeter is 4*side not 4*area
• 10 years agoHelpfull: Yes(0) No(2)
• side of 1st square = 6
  side of 2nd square = 3*2^(1/2)
  like that it forms a GP.
  6,3root(2),1.5.......upto 9th term.
  9th term = 0.34
  perimeter of 9th square = 4*0.34 = 1.38 ans
• 10 years agoHelpfull: Yes(0) No(1)