A square and a equilateral triangle are to be formed out of the same piece of wire. The wire is 6 inches long. How do you maximize the total area the square and the triangle contain?
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To maximize the total area of the square and the equilateral triangle formed from the 6inch wire, we need to use the wire efficiently.

Forming the Square: Since a square has four equal sides, divide the wire into four equal parts, each measuring 6/4 = 1.5 inches. Use these four parts to form the four sides of the square. The area of the square is then side^2, so each side is 1.5 inches, making the area 1.5^2 = 2.25 square inches.

Forming the Equilateral Triangle: An equilateral triangle also has three equal sides. Divide the remaining wire (6  4*1.5 = 0 inches) into three equal parts, each measuring 0 inches. Use these three parts to form the three sides of the equilateral triangle. The area of an equilateral triangle is (side^2 * sqrt(3)) / 4, where side is the length of each side. Since each side is 0 inches, the area of the equilateral triangle is 0 square inches.
Therefore, to maximize the total area contained by the square and the equilateral triangle, we would form only the square, as it has a positive area.
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