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JEE Main Mathematics question

MathematicsApplication of DerivativesJEE Main

Two equilateral triangles are constructed from a line segment of length (the segment is cut into two parts, possibly of zero length, and each part is bent into an equilateral triangle). If and are the maximum and minimum values of the sum of their areas, then the value of is .

Answer: 2

Solution

If one piece has length , the triangles have sides and . Total area

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Question ID VK-008242