Equilateral Triangle Side Lengths

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To find the side lengths of the equilateral triangle represented by the expressions x + 12, 3x - 8, and 2x + 2, set the expressions equal to each other since all sides are equal. This leads to equations like x + 12 = 3x - 8 and x + 12 = 2x + 2, which can be solved to find the value of x. Once x is determined, substitute it back into any of the expressions to find the length of each side. The solution process involves solving for x using algebraic methods rather than a system of equations. Ultimately, this approach will yield the measure of each side of the triangle.
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Homework Statement


Th measure of the sides of an equilateral triangle are represented by x + 12, 3x - 8, and 2x + 2. What is the measure of each side of the triangle.



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The Attempt at a Solution


Well, I know that each side of this triangle are equal, resulting in only one x-value. I first thought of solving them as a system of equations, but then I realized that these are just expressions--they are equal to nothing. How do I solve this?
 
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If A, B and C are the lengths of the side of an equilateral triangle then A=B=C.

Putting two sides equal to each other should give you the desired result.
 
Blimey, thank you so very much for you time and insight.
 

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