A path 1.5 m wide runs all round a square garden, just inside its boundary. The path covers 165 m². What is the length of a side of the garden?

Explanation

1. 01

   Let the side be s. The part inside the path is a square of side $s - 2 \times 1.5 = s - 3$.

2. 02

   Path area = $s^2 - (s - 3)^2 = 6s - 9$.

3. 03

   $6s - 9 = 165$, so $6s = 174$ and $s = 29$ m. Check: $29^2 - 26^2 = 841 - 676 = 165$.