Question

    The sides of a triangle are 15 cm, 20 cm, and 25 cm. A

    smaller triangle is drawn inside it such that its sides are proportional to the original triangle and the ratio of areas of the smaller triangle to the original triangle is 1:16. Find the perimeter of the smaller triangle.
    A 15 cm Correct Answer Incorrect Answer
    B 20 cm Correct Answer Incorrect Answer
    C 25 cm Correct Answer Incorrect Answer
    D 30 cm Correct Answer Incorrect Answer

    Solution

    The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Given the area ratio = 1:16, the side ratio = √1:√16 = 1:4. Perimeter of the original triangle = 15 + 20 + 25 = 60 cm. Perimeter of the smaller triangle = 60 ÷ 4 = 15 cm. Correct answer: a) 15 cm

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