A square has a side of 40 cm. Another square is formed by joining the mid-points of the sides of the given square and this process is repeated infinitely. Find the perimeter of all the squares thus formed.
(a) 160 (1 + √2)
(b) 160 (2 + √2)
(c) 160 (2 – √2)
(d) 160 (1 – √2)
Correct option (b) 160 (2 + √2)
Explanation:
The first perimeter is 160, the second one is 160√2, the third one would be 80 and so on till infinite terms The infinite sum would be equal to 160(2+√2).
