What is the radius of a circular field whose area is equal to the sum of the areas of three smaller circular fields of radii 8 m, 9 m and 12 m, respectively?

17 m

We know that,

Area of a circle = πr²

Radii of three smaller circular fields are 8 m, 9 m, and 12 m.

Let the radius of the larger circular field be r

So, The total area = Sum of all the other areas

= πr² = π(8²) + π(9²) + π(12²)

= πr²  = π(64) + π(81) + π(144)

= πr²  = π(289)

= r² = 289

= r = 17 m