Area and area

Geometry Level 3

Let S 1 , S 2 , S_{1},S_{2}, .....be squares such that for each n greater than equal to 1 the length of a side of S n S_{n} equals the length of a diagonal of S n + 1 S_{n+1} . if the length of a side of S 1 S_{1} is 10cm, then for which of the following values of n is the area of S n S_{n} less than 1 sq.cm ?

5 none 7 8 6

Koushal Kumar by Koushal Kumar , 26, India

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1 solution

Geoff Pilling
Jul 14, 2016

S 1 = 10 S_1 = 10 cm, and S n = S n − 1 2 S_n = \frac{S_{n-1}}{\sqrt{2}}

So, S 8 < 1 S_8 < 1 cm, so S n 2 < 1 c m 2 S_n^2< 1 cm^2 for n = 8 n=\boxed8

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