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.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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