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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Medium

Triangle $A B C$ is similar to triangle $X Y Z$ , such that $A$ , $B$ , and $C$ correspond to $X$ , $Y$ , and $Z$ respectively. The length of each side of triangle $X Y Z$ is $2$ times the length of its corresponding side in triangle $A B C$ . The measure of side $A B$ is $16$ . What is the measure of side $X Y$ ?

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Explanation

Choice D is correct. It's given that triangle $A B C$ is similar to triangle $X Y Z$ , such that $A$ , $B$ , and $C$ correspond to $X$ , $Y$ , and $Z$ , respectively. Therefore, side $A B$ corresponds to side $X Y$ . Since the length of each side of triangle $X Y Z$ is $2$ times the length of its corresponding side in triangle $A B C$ , it follows that the measure of side $X Y$ is $2$ times the measure of side $A B$ . Thus, since the measure of side $A B$ is $16$ , then the measure of side $X Y$ is $2 left parenthesis 16 right parenthesis$ , or $32$ .

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

Choice B is incorrect. This is the measure of side $A B$ , not side $X Y$ .

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