Multiple choice

If the ratio of areas of two circles is 144 : 225, what is the ratio of their radii?

  1. 15 : 12

  2. 12 : 15

  3. 144 : 225

  4. 225 : 144
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B Correct answer
Explanation

The ratio of areas of two circles is the square of the ratio of their radii. If A1/A2 = 144/225, then r1/r2 = sqrt(144/225) = 12/15.

AI explanation

The area of a circle is proportional to the square of its radius, meaning the ratio of the radii is the square root of the ratio of the areas. Taking the square root of the given area ratio 144 : 225 gives the radius ratio as 12 : 15.

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