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The correct answer is $35$. It’s given that the perimeter of an isosceles triangle is $83$ inches and that each of the two congruent sides has a length of $24$ inches. The perimeter of a triangle is the sum of the lengths of its three sides. The equation $24+24+x=83$ can be used to represent this situation, where $x$ is the length, in inches, of the third side. Combining like terms on the left-hand side of this equation yields $48+x=83$. Subtracting $48$ from both sides of this equation yields $x=35$. Therefore, the length, in inches, of the third side is $35$.