Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter P and area A of the smaller triangle.

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  1. Since S2/S1 = 8/12 = 2/3,
    P2/P1 = 2/3
    A2/A1 = (2/3)^2

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  2. the side length of the smaller triangle is 2/3 that of the larger triangle

    so the perimeter of the smaller triangle is 2/3 the perimeter of the larger triangle

    and the area of the smaller triangle is (2/3)^2 the area of the larger triangle

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