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Algebra / Linear equations in two variables Difficulty: Medium

$2 x + y = 37$

In triangle $Q R S$ , sides $Q R$ and $R S$ each have a length of $x$ centimeters and side $S Q$ has a length of $y$ centimeters. The given equation represents this situation. Which of the following is the best interpretation of $37$ in this context?

The difference, in centimeters, between the lengths of sides $Q R$ and $S Q$

The difference, in centimeters, between the lengths of sides $Q R$ and $R S$

The sum of the lengths, in centimeters, of the three sides of the triangle

The length, in centimeters, of one of the two sides of equal length

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Explanation

Choice C is correct. It's given that in triangle $Q R S$ , sides $Q R$ and $R S$ each have a length of $x$ centimeters. Therefore, the expression $2 x$ represents the sum of the lengths, in centimeters, of sides $Q R$ and $R S$ . It's also given that side $S Q$ has a length of $y$ centimeters. Therefore, the expression $2 x plus y$ represents the sum of the lengths, in centimeters, of sides $Q R$ , $R S$ , and $S Q$ . Since $2 x plus y$ is the sum of the lengths, in centimeters, of the three sides of the triangle and $2 x + y = 37$ , 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 $Q R$ and $S Q$ is $x - y$ , not $37$ .

Choice B is incorrect. The difference, in centimeters, between the lengths of sides $Q R$ and $R S$ 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 $37$ .