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Let S(1) be the sum of areas of the squa...

Let `S_(1)` be the sum of areas of the squares whose sides are parallel to coordinates axes
Let `S_(2)` be the sum of areas of the slanted squares as shown in the figure. Then `S_(1)//S_(2)` is

A

2

B

`sqrt2`

C

1

D

`1/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
a
`S_(1)=a^(2)+(a^(2))/4+a^(2)/16+...... infty= a^(2)/(1-1/4)=(4a^(2))/3`
`S_(2)(a^(2))/2+a^(2)/8+a^(2)/32+...... infty=(a^(2)/2)/(1-1/4)=(4a^2)/6`
`(S_(1))/(S_(2))=2`
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