Question

Let $S_1$ be a square of side a. Another square $S_2$ is formed by joining the mid-points of the sides of $S_1$. The same process is applied to $S_2$ to form yet another square $S_3$, and so on. If $A_1,A_2,A_3$, ……… be the areas and $P_1,P_2,P_3$, ……… be the perimeters of $S_1,S_2,S_3$, ……., respectively, then the ratio $\frac{(P_1+P_2+P_3+P_4+\dots )}{(A_1+A_2+A_3+A_4+\dots )}$ equals :

• A. $\frac{2(1+\sqrt{2})}{a}$
• B. $\frac{2(2-\sqrt{2})}{a}$
• C. $\frac{2(2+\sqrt{2})}{a}$
• D. $\frac{2(1+2\sqrt{2})}{a}$

Answer 1

The correct option is C $\frac{2(2+\sqrt{2})}{a}$

Option (C) is the correct answer. Check the video for the approach.