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 $12m, 9m$ and $8m$ respectively?

Using the circle area formula, pi times radius squared, the area of the larger circle equals the sum of the areas of the three smaller circles. This means pi times the large radius squared equals pi times 12 squared plus pi times 9 squared plus pi times 8 squared. Dividing by pi gives the large radius squared equals 144 plus 81 plus 64, which is 289. Taking the square root gives the radius as 17 meters.

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