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Geometry and Trigonometry Difficulty: Medium

Each side of equilateral triangle S is multiplied by a scale factor of $k$ to create equilateral triangle T. The length of each side of triangle T is greater than the length of each side of triangle S. Which of the following could be the value of $k$ ?

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Explanation

Choice A is correct. It's given that each side of equilateral triangle S is multiplied by a scale factor of $k$ to create equilateral triangle T. Since the length of each side of triangle T is greater than the length of each side of triangle S, the scale factor of $k$ must be greater than $1$ . Of the given choices, only $StartFraction 29 Over 28 EndFraction$ is greater than $1$ .

Choice B is incorrect. If each side of equilateral triangle S is multiplied by a scale factor of $1$ , the length of each side of triangle T would be equal to the length of each side of triangle S.

Choice C is incorrect. If each side of equilateral triangle S is multiplied by a scale factor of $StartFraction 28 Over 29 EndFraction$ , the length of each side of triangle T would be less than the length of each side of triangle S.

Choice D is incorrect and may result from conceptual or calculation errors.