Multiple choice

If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?

  1. 14 : 25

  2. 13 : 20

  3. 14 : 20

  4. 13 : 25
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A Correct answer
Explanation

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides. If area ratio is 196:625, side ratio is sqrt(196):sqrt(625) = 14:25.

AI explanation

By the property of similar triangles, the ratio of the areas is equal to the square of the ratio of the corresponding sides. Taking the square root of the given area ratio of 196 : 625 gives the side ratio. The square root of 196 is 14, and the square root of 625 is 25. The ratio of the corresponding sides is 14 : 25.

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