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Two similar triangles have perimeters in the ratio 4:7. If the sum of their areas is 130 cm², find the area of the smaller triangle.

1. 16 cm²
2. 49 cm²
3. 32 cm²
4. 64 cm²

Correct answer: 32 cm²

Solution

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides, so the side ratio is 4:7. Therefore, the area ratio is 16:49, and the total 130 cm² is divided in this ratio, giving the smaller area as 32 cm².

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