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Консультация № 199865
14.12.2020, 14:23
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Здравствуйте! Прошу помощи в следующем вопросе:
Площадь равнобедренной трапеции равна 180 кв. см. Найти длину верхнего основания, если боковые стороны равны по 13 см, а нижнее основание - 20 см.
У меня получилось решить задачу только уравнением 4ой степени, хотелось бы найти какое-то более простое решение.(Задача 8 класса)
Площадь равнобедренной трапеции равна 180 кв. см. Найти длину верхнего основания, если боковые стороны равны по 13 см, а нижнее основание - 20 см.
У меня получилось решить задачу только уравнением 4ой степени, хотелось бы найти какое-то более простое решение.(Задача 8 класса)
Обсуждение
19.12.2020, 14:10
общий
это ответ
Здравствуйте, lyskov.kirill!
Если a и b - нижнее и верхнее основание трапеции, c - её боковая сторона и h - высота, то выполняются следующие соотношения:
или, если положить d = (a-b)/2,
В данном случае, для S = 180 см[sup]2[/sup], a = 20 см и c = 13 см получаем систему
Её действительно можно решить с помощью уравнения четвёртой степени, но проще подобрать нужные значения h и d, которые скорее всего будут парой целых чисел. Очевидно, что h>0, d>0, из второго уравнения следует h<13, а из первого - h>9. Единственные значения, удовлетворяющие обоим уравнениям - h = 12 см и d = 5 см, откуда b = a - 2d = 10 см.
Если a и b - нижнее и верхнее основание трапеции, c - её боковая сторона и h - высота, то выполняются следующие соотношения:
или, если положить d = (a-b)/2,
В данном случае, для S = 180 см[sup]2[/sup], a = 20 см и c = 13 см получаем систему
Её действительно можно решить с помощью уравнения четвёртой степени, но проще подобрать нужные значения h и d, которые скорее всего будут парой целых чисел. Очевидно, что h>0, d>0, из второго уравнения следует h<13, а из первого - h>9. Единственные значения, удовлетворяющие обоим уравнениям - h = 12 см и d = 5 см, откуда b = a - 2d = 10 см.
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