Бічні сторони трапеції 15 см і 20 см а різниця їх основ 25 см Знайти висоту трап...

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Бічні сторони трапеції 15 см і 20 см а різниця їх основ 25 см
Знайти висоту трапеції
С полным решением и рисунком , пожалуйста.

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NNNLLL54

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Ответ:

АВСД - трапеция, АВ=15 , СД=20 , АД-ВС=25

Проведём ВМ || СД ⇒ так как ВС || АД , то ВСДМ - параллелограмм и ВМ=СД=20 и ВС=МД .

ΔАВМ: АМ=АД-МД=АД-ВС=25

Найдём площадь этого треугольника по формуле Герона.

$p=\frac{15+20+25}{2}=30\\\\S(ABM)=\sqrt{30(30-15)(30-20)(30-25)}=\sqrt{30\cdot 15\cdot 10\cdot 5}=150$

Теперь вычислим площадь этого треугольника по стороне и высоте. Высота треугольника АВМ совпадает с высотой трапеции.

$S(ABM)=\frac{1}{2}\cdot AM\cdot BH=\frac{1}{2}\cdot 25\cdot h=150\\\\h= \frac{150\cdot 2}{25}=12$

Ответ: h=12 см .

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