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Inscribing five squares

Source: 2004 Korea Junior Math Olympiad

June 28, 2024
geometryKMOinequalities

Problem Statement

For positive reals a1,a2,...,a5a_1, a_2, ..., a_5 such that a12+a22+...+a52=2a^2_1+a^2_2+...+a^2_5=2, consider five squares with sides a1,a2,...,a5a_1, a_2, ..., a_5 respectively. Show that these squares can be placed inside (including boundaries) a square with side length of 22 so that the square themselves do not overlap each other.
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