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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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grujan50

Answer:

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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