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Geometry and Trigonometry Difficulty: Easy

In the figure shown, triangle $J K L$ is similar to triangle $R S T$ , where $J$ corresponds to $R$ and $K$ corresponds to $S$ . The length of $\bar{J K}$ is $15$ , and the perimeter of triangle $J K L$ is $36$ . The length of $\bar{R S}$ is $135$ . What is the perimeter of triangle $R S T$ ?

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Explanation

Choice A is correct. It’s given that triangle $J K L$ is similar to triangle $R S T$ , where $J$ corresponds to $R$ and $K$ corresponds to $S$ . It follows that $\bar{J K}$ corresponds to $\bar{R S}$ . If two triangles are similar, then the scale factor between their perimeters is equal to the scale factor between the lengths of their corresponding sides. It's given that the length of $\bar{J K}$ is $15$ and the length of $\bar{R S}$ is $135$ . Therefore, the scale factor from the length of $\bar{J K}$ to the length of $\bar{R S}$ is $StartFraction 135 Over 15 EndFraction$ , or $9$ . It’s given that the perimeter of triangle $J K L$ is $36$ . Let $p$ represent the perimeter of triangle $R S T$ . It follows that $\frac{p}{36} = 9$ . Multiplying each side of this equation by $36$ yields $p equals 324$ . Therefore, the perimeter of triangle $R S T$ is $324$ .

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

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

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