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Консультация № 187742
12.02.2014, 19:49
79.10 руб.
0
4
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос: Высота пирамиды разделена на 4 равные части и через точки деления проведены плоскости, параллельные основанию. Площади полученных сечений равны 25, 100 и 225 кв.ед. Определить площадь основания. Заранее благодарен.
Обсуждение
12.02.2014, 19:54
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Площади сечений пропорциональны квадратам высот полученных пирамид. В данном случае имеем 52:102:152, высоты относятся как 1:2:3, значит высота всей пирамиды равна учетверенной высоте самой меньшей, основание равно 202=400
Площади сечений пропорциональны квадратам высот полученных пирамид. В данном случае имеем 52:102:152, высоты относятся как 1:2:3, значит высота всей пирамиды равна учетверенной высоте самой меньшей, основание равно 202=400
Неизвестный
12.02.2014, 20:05
общий
12.02.2014, 20:06
Адресаты:
Любая из проведенных плоскостей отсекает пирамиду, подобную исходной. Соответственные высоты относятся как коэффициент подобия, а площади соответствующих оснований --- как квадрат коэффициента подобия. Возьмем сечение площади 100, проведенное через середину высоты. Тогда k = 2, и значит площадь основания равна 100k^2 = 400
14.02.2014, 03:49
общий
Адресаты:
Тимофеев Алексей Валентинович Здравствуйте! Поясните, пожалуйста, как получилось 20.
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