A square garden is surrounded by a path of uniform width 3 meters. If the area of the path is 84 square meters, find the side length of the garden.

Question: A square garden is surrounded by a path of uniform width 3 meters. If the area of the path is 84 square meters, find the side length of the garden. Solution:Let the side of the garden = x meters.Then, the side of the garden including the path = x + (2 × 3) = x + 6 meters. Area of path = Area of garden with path - Area of garden⇒ 84 = (x + 6)2 - x2⇒ 84 = x2 + 12x + 36 - x2 ⇒ 12x + 36 = 84⇒ 12x = 84 - 36⇒ x = 48/12 ∴ x = 4 meters ∴ Therefore, side length of the garden is 4 meters.