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Direction: Answer the following questions based on following data.
A square has a side of 30 cm. Another smaller square is formed by joining the mid-points of the given square, and this process is repeated infinitely.
Find the sum of the areas of all the squares thus formed, including the initial square?
  • a)
    900 cm2
  • b)
    1350 cm2
  • c)
    1800 cm2
  • d)
    3600 cm2
Correct answer is option 'C'. Can you explain this answer?
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Direction: Answer the following questions based on following data.A s...
Since every smaller square is formed by joining the mid-points of the given square, the side of the smaller square formed inside is always 1/√2 of the side of the bigger square.
By Pythagoras Theorem, if the side of the outer square is 'a', side of the inner square formed will be
√ [(a/2)2 + (a/2)2] = √ [a2/4 + a2/4] = a/√2
So we can see that the sides of every subsequent square formed form a G.P. Series, with
a = 30 and r = 1/√2
Area of Initial Square(A) = a2 = 900 cm, and every subsequent square has area diminished by a factor of 1/2. So sum of all Areas = A/(1 - r) = 900/(1 - 1/2) = 1800 cm2
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Direction: Answer the following questions based on following data.A square has a side of 30 cm. Another smaller square is formed by joining the mid-points of the given square, and this process is repeated infinitely.Find the sum of the areas of all the squares thus formed, including the initial square?a)900 cm2b)1350 cm2c)1800 cm2d)3600 cm2Correct answer is option 'C'. Can you explain this answer?
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