Предмет: Алгебра, автор: vasilinapipak

У трикутнику ABC проведено висоту BD (точка D лежить на продовженні сторони AC, точка A лежить між точками D і C) BC=39см, BD=15см, AB=17см. Знайти периметр ABC.

Ответы

Автор ответа: OkiD0ki

6

Ответ:

100см

Объяснение:

Так как BD высота, она перпендикулярна основанию АС. Отсюда треугольники BDC и BDA прямоугольные. Опираясь на теорему Пифагора, найдём длину отрезков DC и АD. Пускай DC =х, отсюда:

15 ² +х ² =39 ²

х ² = 39 ² -15 ²

х ² = 1296

х =√1296

х= 36 см.

Пускай АD = у, отсюда:

15² + у² = 17²

у² = 17² - 15²

у² =64

у = √64

у = 8 см.

Найдём длину стороны АС:

АС = DC + АD

АС = 36 + 8

АС = 44 см.

Теперь можно найти периметр треугольника АВС:

Р▲АВС = 17+ 39 + 44 = 100см.

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