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The ratio of the product of the sides of an equilateral triangle to its perimeter is equal to the ratio of the product of the sides of another equilateral triangle to its perimeter. Then the triangles are

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Let the sides of the triangles be x and y.
Given `(x^(3))/(3x)=(y^(3))/(3y)`
`x^(2)=y`
`x=y`
`:.` Both the triangles are congruent.
`:.` They are similar.

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