2 x + y = 37 In triangle Q R S , sides Q R and

Choice C is correct. It's given that in triangle $QRS$, sides $QR$ and $RS$ each have a length of $x$ centimeters. Therefore, the expression $2x$ represents the sum of the lengths, in centimeters, of sides $QR$ and $RS$. It's also given that side $SQ$ has a length of $y$ centimeters. Therefore, the expression $2x+y$ represents the sum of the lengths, in centimeters, of sides $QR$, $RS$, and $SQ$. Since $2x+y$ is the sum of the lengths, in centimeters, of the three sides of the triangle and $2x+y=37$, it follows that $37$ is the sum of the lengths, in centimeters, of the three sides of the triangle.

Choice A is incorrect. The difference, in centimeters, between the lengths of sides $QR$ and $SQ$ is $x-y$, not $37$.

Choice B is incorrect. The difference, in centimeters, between the lengths of sides $QR$ and $RS$ is $x-x$, or $0$, not $37$.

Choice D is incorrect. The length, in centimeters, of one of the two sides of equal length is $x$, not $37$.