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21 February, 16:09

Two triangle are similar. The side of one are three times as long as the sides of the other. What is the ratio of the areas of the smaller to the larger?

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  1. 21 February, 16:14
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    Correct answer: A₁ : A = 1 : 9

    Step-by-step explanation:

    Given: a = 3 a₁

    Side of the first triangle let be a and of the second a₁

    Area of the first triangle let be A and of the second A₁

    If the two triangles are similar then it is:

    A₁ : A = a₁² : a²

    A₁ : A = a₁² : (3 a₁) ² = a₁² : 9 a₁² = 1 : 9

    A₁ : A = 1 : 9

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