Предмет: Геометрия, автор: evaasp

7 класс, 80 баллов!
Боковая сторона равнобедренного треугольника делится точкой касания вписанной окружности в отношении 4 : 5, считая от вершины угла при основании треугольника. Найдите стороны треугольника, если его периметр равен 104 см.

Ответы

Автор ответа: UncleGreg

Ответ:

Боковые стороны: a = 36 см

Основание: b = 32 см

Объяснение:

Пусть боковая сторона

a = 5x + 4x = 9x

Для вписанной фигуры отрезки касательных от пересечения касательных до т. касания равны. Нам известно, что такой отрезок боковой стороны от основания до т. касания = 4x. Тогда длина основания b = 4x + 4x = 8x

Периметр равнобедренного треугольника

P = 2*a + b = 2*(5x + 4x) + (4x + 4x) = 2*9x + 8x = 26x = 104 см

x = 4 см

Боковые стороны: a = 5x + 4x = 9*4 = 36 см

Основание: b = 4x + 4x = 8*4 = 32 см

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