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Консультация № 146234
06.10.2008, 18:50
0.00 руб.
06.10.2008, 19:05
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Уважаемые Эксперты,помогите пожалуйста решить задачу:. Острый угол параллелограмма ABCD равен α, высота, опущенная из вершины тупого угла ABC на большую сторону AD, равна h. Найти меньшую диагональ параллелограмма, если ВС=2АВ.
Обсуждение
Неизвестный
10.10.2008, 07:35
общий
это ответ
Здравствуйте, Irokez!
высота а опущена а сторону АД в точке Е
искомая диагональ ВД=V(a^2+(ЕD)^2), V - корень квадратный (1)
ED=2b-AE
AE=V(b^2-a^2)
ED=2b-V(b^2-a^2)
подставляем полученное в выражение (1)
BD=V(a^2+(2b-V(b^2-a^2))^2)=V(a^2+4b^2-4bV(b^2-a^2)+b^2-a^2
упростив, получаем
BD=V(5b^2-4bV(b^2-a^2))
Приложение:
высота а опущена а сторону АД в точке Е
искомая диагональ ВД=V(a^2+(ЕD)^2), V - корень квадратный (1)
ED=2b-AE
AE=V(b^2-a^2)
ED=2b-V(b^2-a^2)
подставляем полученное в выражение (1)
BD=V(a^2+(2b-V(b^2-a^2))^2)=V(a^2+4b^2-4bV(b^2-a^2)+b^2-a^2
упростив, получаем
BD=V(5b^2-4bV(b^2-a^2))
Приложение:
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