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Geometry and Trigonometry Difficulty: Easy

The perimeter of triangle $A B C$ is $17$ inches, the length of side $A B$ is $4$ inches, and the length of side $A C$ is $7$ inches. What is the length, in inches, of side $B C$ ?

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Explanation

Choice B is correct. The perimeter of a triangle is the sum of the lengths of all three sides of the triangle. It’s given that the lengths of side $A B$ and side $A C$ are $4$ inches and $7$ inches, respectively. Let $x$ represent the length, in inches, of side $B C$ . The sum of the lengths, in inches, of all three sides of triangle $A B C$ can be represented by the expression $4 + 7 + x$ . Since it’s given that the perimeter of triangle $A B C$ is $17$ inches, it follows that $17 = 4 + 7 + x$ , or $17 = 11 + x$ . Subtracting $11$ from both sides of this equation yields $6 equals x$ . Therefore, the length, in inches, of side $B C$ is $6$ .

Choice A is incorrect. This is the length, in inches, of side $A B$ .

Choice C is incorrect. This is the length, in inches, of side $A C$ .

Choice D is incorrect. This is the sum of the lengths, in inches, of sides $A B$ and $A C$ .