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Консультация № 146107
05.10.2008, 17:40
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Пожалуйста,помогите решть задачу.
В выпуклом четырёхугольнике MNLQ углы при вершинах N и L прямые, а величина угла при вершине М равна 60°. Найти длину диагонали NQ, если известно, что длина стороны LQ вдвое меньше длины стороны MN и на 2 м больше стороны LN.
В выпуклом четырёхугольнике MNLQ углы при вершинах N и L прямые, а величина угла при вершине М равна 60°. Найти длину диагонали NQ, если известно, что длина стороны LQ вдвое меньше длины стороны MN и на 2 м больше стороны LN.
Обсуждение
Неизвестный
05.10.2008, 18:04
общий
это ответ
Здравствуйте, Артемьев Дмитрий Михайлович!
Очевидно, что MNLQ прямоугольная трапеция, где MN и LQ основания. Тогда возьмем LQ =х. Тогда MN=2х, а LN=х+2. Проведем из точки Q высоту на основание MN назовем точку пересечения скажем Н. НМ будет равна х.(это очевидно). QН=LN=х+2. Возьмем треугольник МQН. Он прямоугольный. Так как QН напротив угла в 60 градусов то QН=2НМ то есть х+2=2х откуда получаем, что х=2. Из треугольника NLQ: QN в квадрате равняется сумме квадратов LN и LQ. Задача решена.
Очевидно, что MNLQ прямоугольная трапеция, где MN и LQ основания. Тогда возьмем LQ =х. Тогда MN=2х, а LN=х+2. Проведем из точки Q высоту на основание MN назовем точку пересечения скажем Н. НМ будет равна х.(это очевидно). QН=LN=х+2. Возьмем треугольник МQН. Он прямоугольный. Так как QН напротив угла в 60 градусов то QН=2НМ то есть х+2=2х откуда получаем, что х=2. Из треугольника NLQ: QN в квадрате равняется сумме квадратов LN и LQ. Задача решена.
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