A rectangular field is $80$ m long and $60$ m wide. A path $5$ m wide runs all around it inside the field.…

A rectangular field is $80$ m long and $60$ m wide. A path $5$ m wide runs all around it inside the field. Find the area of the path.
  1. $1300 \text{ m}^{2}$
  2. $1500 \text{ m}^{2}$
  3. $1200 \text{ m}^{2}$
  4. $1400 \text{ m}^{2}$

Solution

Outer area $= 80 \times 60 = 4800$. Inner field $= (80-10)\times(60-10) = 70 \times 50 = 3500$. Path area $= 4800 - 3500 = 1300 \text{ m}^{2}$.

Asked in: IMO

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