Вопрос школьника по предмету Геометрия
в трапеции авсд с основаниями ад и вс диагонали пересекаются в точке о.Площадь треугольника ВОС равна 3 , а площадь треугольника АОД равна 27 . Найдите АС , если АО=6
Ответ учителя по предмету Геометрия
итак- треугольники АОД и ВОС подобны и соответствующие стороны подобны. , т.е. АО подобно ОС.
А с каким коэфф.? А вот здесь вспоминаем (либо запоминаем ) — отношение площадей равно отношению квадратов соответствующих линейных величин. ( это легко доказать либо понять- площадь — это умножить одну величину на другую.)
коэфф подобия площадей = 27/3=9 — площади относятся как 9:1, тогда коэфф. подобия линейных величин( сторон, высот) будет √9 т.е. 3
Значит, АО:ОС=3
откуда ОС =АО/3=6/3= 2
тогда АС=АО+ОС=6+2=8
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Д)тратуары заливают асвалтом.
Памогите пожалста завтра экзамен