Предмет: Геометрия, автор: ololoshiksev

Основания равнобедренной трапеции равны 18 и 30 , а её площадь равна 192. Найдите периметр трапеции.

Ответы

Автор ответа: Streetdancer152
4

Обозначим трапецию ABCD , а высоту  CH. Формула площади трапеции  S = (<var>\frac{a+b}{2}*h</var>a+b/2)* . <var>192 = \frac{18+30}{2} * h</var> следовательно 192=24*h . h=8.   CH=8, HD= 6. Из треугольника CHD : <var>CD^{2} = CH^{2} + HD^{2} CD^{2} = 64+36</var> СD = 10. P = BC + 2CD + AD. Следовательно Р= 18 + 20 +30 = 68 .

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