2
Question
Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3, ……… be the areas and P1, P2, P3, ……… be the perimeters of S1, S2, S3, ……., respectively, then the ratio 
equals :(CAT 2003)
Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3, ……… be the areas and P1, P2, P3, ……… be the perimeters of S1, S2, S3, ……., respectively, then the ratio equals :(CAT 2003)
Open in App
Solution
The correct option is C
Option (c)
From the given condition in question
Area and perimeter of S1 = a2, 4a
Area and perimeter of S2 = 
Area and perimeter of S3 =
Area and perimeter of S4 
These are 2 infinite GPs , which can be solved as follows
Required ratio
=
=
= 
→ 
→ 
Option (c)
From the given condition in question
Area and perimeter of S1 = a2, 4a
Area and perimeter of S2 =
Area and perimeter of S3 =
Area and perimeter of S4
These are 2 infinite GPs , which can be solved as follows
Required ratio
=
=
= → →
Suggest Corrections
0
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
