There is a square of side x cm Another square is made by joining the mid points of sides of that squ...........

Quantitative Aptitude ( CCS) Mensuration 2D

There is a square of side x cm. Another square is made by joining the mid-points of sides of that square and this process is repeated infinitely. If the perimeter of all the squares thus formed is 120(2+(2)^1/2) cm, find the value of x.

50 cm

30 cm

60 cm

40 cm

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Explanation:

Perimeter of square1 = 4x cm
Length of the square made by joining the mid-points of square1 = [(x/2)^2 + (x/2)^2]^1/2 = x/(2)^1/2 cm
Perimeter of the square = 4*x/(2)^1/2 cm
Now, 4x+4*x/(2)^1/2 + … to infinity = 120(2+(2)^1/2)
=> 4*x/(1 – 1/(2)^1/2) = 120(2+(2)^1/2)
=> x = 30 cm