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Answer 1

Topic :-

Ratio

Given :-

A square ABCD inscribes the largest possible circle in it. This circle has the largest possible square PQRS inscribed in it.

To Find :-

Ratio of perimeters of squares PQRS and ABCD.

Formula to be Used :-

Perimeter of Square = 4 × Side

Length of Diagonal of a Square = (Side)√2

Solution :-

Let 'a' be the side of square ABCD.

Let O be the centre of Circle and 'r' be its radius.

We can clearly see that,

a = 2r

Now,

Let a' be the side of square PQRS.

OQ = r

OQ is half the length of diagonal of square PQRS.

OQ = a' / √2

r = a' / √2

a' = r√2

Taking ratio of Perimeter of Squares PQRS and ABCD.

4a' : 4a

a' : a

r√2 : 2r

1 : √2

Answer :-

So, the ratio of perimeter of squares PQRS and ABCD is 1 : √2 which is option A.