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A wire of length L style=”color:rgb(0,0,0);background-color:rgb(255,228,181);”> is cut at the red point. The segment to the left of the cut is formed into an equilateral triangle, and the segment to the right of the cut is formed into a square. Let x be the length of the segment to the left of the cut. What value of x maximizes the total area of the two shapes? What value of x minimizes the total area?

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A wire of length L

style=”color:rgb(0,0,0);background-color:rgb(255,228,181);”> is cut at the red point. The segment to the left of the cut is formed into an equilateral triangle, and the segment to the right of the cut is formed into a square. Let x be the length of the segment to the left of the cut. 

What value of x maximizes the total area of the two shapes? What value of x minimizes the total area?

 
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