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(#M40024840) SELF question Keep an EYE

A Square of side 5 cm .the midpoints are joined to form a smaller square.this process is repeated.What will be the perimeter of 9th square?

Arneet Singh (11 years ago)

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Asit Shukla  (11 years ago)

2nd inner sq:side=5/sqrt2*1
3rd inner sq:side=5/sqrt2*2
4th inner sq:side=5/sqrt2*3
..
..
..
9th inner sq:side=5/sqrt2*8
=5/4 ans

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chandan kumar  (11 years ago)

area of square = a^2;
1). area of square after joining midpoints = (a^2)/2;
2). area of square after joining midpoints of square constructed in step 1=((a^2)/2)/2 i.e (a^2)/4.
hence in 9th step area of square would be (a^2)/2^9=(a^2)/512.
and perimeter will be 4*sqrt((a^2)/512).

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