Multiple choice

The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

  1. $625:256$
  2. $5:6$
  3. $25:16$
  4. $5:4$
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D Correct answer
Explanation

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides (or perimeters). If Area1/Area2 = 25/16, then Perimeter1/Perimeter2 = sqrt(25/16) = 5/4.

AI explanation

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides or perimeters. Taking the square root of the given area ratio of 25 to 16 yields 5 divided by 4. Thus, the ratio of their perimeters is 5:4.

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