У задачи выше есть разные решения — например, такое:
Будем считать сторону квадрата равной 1. Если одна из сторон прямоугольника равна A, то его площадь не больше A (ведь вторая сторона не больше 1). Поэтому суммарна длина отмеченных отрезков не меньше суммарной площади всех прямоугольников, т.е. 1.
Задача, кстати, была на ММО и на Турнире городов, предложил ее В.В.Произволов.
У задачи выше есть разные решения — например, такое:
Будем считать сторону квадрата равной 1. Если одна из сторон прямоугольника равна A, то его площадь не больше A (ведь вторая сторона не больше 1). Поэтому суммарна длина отмеченных отрезков не меньше суммарной площади всех прямоугольников, т.е. 1.
Задача, кстати, была на ММО и на Турнире городов, предложил ее В.В.Произволов.
BY Геометрия-канал
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