A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares such formed (in sq.cm.)is

(a) 128

(b) 120

(c) 96

(d).None of these

• Answer is option (a) 128
  
  Given Initial Square side is 8cm
  By joining the mid points the side of thus square formed would be squareroot(32)
  (that can be found by using as
  8/2=4 since the square formed is joining midpoint and by applying Pythagoras Theorem to it we get it as sqrt(32))
  and next sides will be as 4,
  next of it will be as sqrt(8), next 2, next sqrt(2), next 1......
  
  for 8x8 square area is 64
  for sqrt(32)xsqrt(32) area is 32
  for 4x4 square area is 16
  for sqrt(8)xsqrt(8) area is 8
  for 2x2 square area is 4
  for sqrt(2)xsqrt(2) area is 2
  for 1x1 square area is 1
  for 0.5x0.5 square area is 0.25
  .
  .
  adding them we get 64+32+16+8+4+2+1+0.25+......
  this will sum to 127.25... which is approximately equal to 128
• 10 years agoHelpfull: Yes(1) No(0)