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ASU 365 All Soviet Union MO 1983 4 rectangles inside rectangle, area inequality

Source:

July 28, 2019
geometryrectanglegeometric inequalityinequalitiesareas

Problem Statement

One side of the rectangle is 11 cm. It is known that the rectangle can be divided by two orthogonal lines onto four rectangles, and each of the smaller rectangles has the area not less than 11 square centimetre, and one of them is not less than 22 square centimetres. What is the least possible length of another side of big rectangle?