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Extrema of area of triangle

Source: Czech and Slovak Olympiad 1961, National Round, Problem 4

June 16, 2024
geometryEquilateralTrianglecomputationtriangle areamaxmin

Problem Statement

Consider a unit square ABCDABCD and a (variable) equilateral triangle XYZXYZ such that X,ZX, Z lie on rays AB,DC,AB, DC, respectively, and YY lies on segment ADAD. Compute the area of triangle XYZXYZ in terms of x=AXx=AX and determine its maximum and minimum.
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