If the width of the path around a square field is 4.5 m and the area of the path is 252 m², then the length of the side of the field is:

Given:

Width of the path around a square field = 4.5 m

Area of the path = 252 m²

Formula used:

Area of square = a²

Where, a = side of the square

Calculation:

Let the side of the square field be a

The side of the square field with path = (a + 4.5 + 4.5) = a + 9

Area of square field = a² ....(1)

Area of the square field with path = (a + 9)² ....(2)

Now,

Area of path = Area of the square field with path –  Area of square field

⇒ 252 = (a + 9)² – a²

⇒ 252 = a² + 81 + 18a – a²

⇒ 252 = 81 + 18a

⇒ 18a = 252 – 81

⇒ 18a = 171

⇒ a = 9.5 m

∴ The length of the side of the field is 9.5 m