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square is cut into rectangles with // sides, sum of ratio of sides >=1

Source: Singapore Junior Math Olympiad 2017 2nd Round p1 SMO

March 26, 2020
geometryrectangleratioGeometric Inequalitiesinequalitiessquaresidelenghts

Problem Statement

A square is cut into several rectangles, none of which is a square, so that the sides of each rectangle are parallel to the sides of the square. For each rectangle with sides a,b,a<ba, b,a<b, compute the ratio a/ba/b. Prove that sum of these ratios is at least 11.
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