Предмет: Геометрия, автор: anulkrptn

диагонали равнобедренной трапеции взаимно перпендикулярны, площадь равна 5,76 дм в квадрате. найдите высоту и среднюю линию.

Ответы

Автор ответа: siestarjoki

2

Диагонали равнобедренной трапеции образуют на основаниях два равнобедренных треугольника, △AOD, △BOC. В равнобедренных треугольниках высота является медианой, медиана из прямого угла равна половине гипотенузы - высоты в треугольниках △AOD, △BOC равны половинам оснований AD и BC. Следовательно, высота данной трапеции равна полусумме оснований, то есть средней линии, h=m.

S=mh =m^2 <=> m=√S

m=h =√5,76 =2,4 (дм)

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