If each side of a square is increased by $10\%$, by what percent does its area increase?

If each side of a square is increased by $10\%$, by what percent does its area increase?
  1. $10\%$
  2. $20\%$
  3. $21\%$
  4. $100\%$

Solution

Let original side $= a$. New side $= 1.1 a$. New area $= 1.21 a^{2}$. Increase $= 0.21 a^{2}$, i.e. $21\%$.

Asked in: IMO

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