The perimeter of triangle A B C is 17 inches, the length of side A B

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

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

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

Choice D is incorrect. This is the sum of the lengths, in inches, of sides $AB$ and $AC$.