Multiple choice

The ratio of the heights of two similar triangles is 3 : 4. If the area of the smaller triangle is 27 square centimeters, what is the area of the larger triangle?

  1. 36 square centimeters

  2. 45 square centimeters

  3. 48 square centimeters

  4. 64 square centimeters

  5. 72 square centimeters
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C Correct answer
Explanation

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Since the ratio of sides is 3:4, the ratio of areas is 3^2:4^2, which is 9:16. Given the smaller area is 27, the larger area is (27/9) * 16 = 3 * 16 = 48.

AI explanation

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding heights. Setting up the proportion, the larger area divided by 27 equals the square of 4 divided by 3, which is 16 divided by 9. Solving for the larger area gives 27 multiplied by 16 and divided by 9, resulting in 48 square centimeters.

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