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Algebra Difficulty: Easy

The perimeter of an isosceles triangle is $36$ feet. Each of the two congruent sides of the triangle has a length of $10$ feet. What is the length, in feet, of the third side?

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Explanation

Choice C is correct. It’s given that the perimeter of an isosceles triangle is $36$ feet and that each of the two congruent sides has a length of $10$ feet. The perimeter of a triangle is the sum of the lengths of its three sides. The equation $10 + 10 + x = 36$ can be used to represent this situation, where $x$ is the length, in feet, of the third side. Combining like terms on the left-hand side of this equation yields $20 + x = 36$ . Subtracting $20$ from each side of this equation yields $x equals 16$ . Therefore, the length, in feet, of the third side is $16$ .

Choice A is incorrect. This would be the length, in feet, of the third side if the perimeter was $30$ feet, not $36$ feet.

Choice B is incorrect. This would be the length, in feet, of the third side if the perimeter was $32$ feet, not $36$ feet.

Choice D is incorrect. This would be the length, in feet, of the third side if the perimeter was $38$ feet, not $36$ feet.