Multiple choice

Given two similar triangles one of which has twice the perimeter of the other, by what factor is the area of the larger triangle bigger than the smaller?

  1. 2

  2. 4

  3. √2

  4. 2√2
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B Correct answer
Explanation

For similar triangles, the ratio of areas is the square of the ratio of their perimeters. If the perimeter ratio is 2, the area ratio is 2^2 = 4.

AI explanation

For similar triangles, the ratio of their perimeters equals the ratio of their corresponding sides, so the side ratio is 2 to 1. The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Thus, the larger triangle has an area that is 2 squared, or 4, times that of the smaller triangle.

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