Предмет: Геометрия, автор: fedorova1999

Прямая, параллельная стороне AC треугольника ABC, пересекает стороны AB и BC в точках M и H соответственно, MB=2 см, AM=14 см, MH= 4 см. Чему равна длина стороны AC ?

Ответы

Автор ответа: nastyawolk

1) Треугольники MВН и ABC подобны по двум углам ( BMH = BAC и BHM=BCA при параллельных прямых MH и AC и секущих BA и ВС)
2) т.к. МВ=2см, АМ=14 см, то АВ=16 см.
3) Если треугольники МВН и АВС подобны, то АС / МН=АВ / МВ отсюда АС= МН*АВ/МВ= 4*16/2= 32см.
Ответ: 32 см.

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