The path running around a square lawn of side $a$ has uniform width $b$ outside. The area of the path is

The path running around a square lawn of side $a$ has uniform width $b$ outside. The area of the path is
  1. $4b(a + b)$
  2. $4ab$
  3. $(a + 2b)^{2}$
  4. $2b(a + b)$

Solution

Outer side $= a+2b$. Path area $= (a+2b)^{2} - a^{2} = (a+2b-a)(a+2b+a) = 2b(2a+2b) = 4b(a+b)$.

Asked in: IMO

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