Даю 90 балловДве стороны одного треугольника равны 27 см и 48 см, второго треугольника – 18 см и 32 см. Углы между известными сторонами треугольников равны. Найдите меньшее из двух неизвестных сторон треугольников, если их сумма равна 55 см.

Ответ:

Давайте позначимо сторони першого треугольника як "a" і "b" (з "a" = 27 см і "b" = 48 см), і сторони другого треугольника як "c" і "d" (з "c" = 18 см і "d" = 32 см). Угли між відомими сторонами обох треугольників рівні.

Ми знаємо, що сума сторін обох треугольників дорівнює 55 см, тобто:

a + b + c + d = 55

Поширюємо це рівняння:

27 + 48 + 18 + 32 = 125

a + b + c + d = 125

Тепер ми знаємо, що a + b + c + d = 125, і ми шукаємо "x" - менше з двох невідомих сторін. Враховуючи, що a і b - найбільші сторони першого треугольника, і c і d - найменші сторони другого треугольника, ми можемо записати:

x + b + c + d = 125

x = 125 - (b + c + d)

Тепер підставимо відомі значення:

x = 125 - (48 + 18 + 32)

x = 125 - 98

x = 27

Отже, менше з двох неизвестних сторін треугольників дорівнює 27 см.

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