The table gives the perimeters of similar triangles T U V and X Y Z , where T U corresponds

Question

The table gives the perimeters of similar triangles $T U V$ and $X Y Z$ , where $T U$ corresponds to $X Y$ . The length of $T U$ is $18$ .

	Perimeter
Triangle $T U V$	$37$
Triangle $X Y Z$	$333$

What is the length of $X Y$ ?

Accepted Answer

Choice D is correct. It's given that triangle &#160; X Y Z is similar to triangle T U V . Therefore, each side of triangle X Y Z is k times its corresponding side of triangle T U V , where k is a constant. It follows that the perimeter of triangle X Y Z is k times the perimeter of triangle T U V . It's also given that T U &#175; corresponds to X Y &#175; and the length of T U &#175; is 18 . Let x represent the length of X Y &#175; . It follows that x = 18 k . The table shows that the perimeters of triangles T U V and X Y Z are 37 and 333 , respectively. It follows that 333 = 37 k , or 9 = k . Substituting 9 for k in the equation x = 18 k yields x = 18 9 , or x = 162 . Therefore, the length of X Y &#175; is 162 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This is the length of T U &#175; , not the length of X Y &#175; . Choice C is incorrect and may result from conceptual or calculation errors.

Question the-ta