Впрямоугольниках abcd и mnkl сторона ab равна стороне mn. площадь прямоугольника abcd в 5 раз больше площади прямоугольника mnkl. чему равна длина отрезка bc , если известно, что длина отрезка nk равна 12 мм.

пусть s это плошадь, тогда s1 площадь  прямоугольника  abcd, а s2  площадь  прямоугольника  mnkl, пусть х это сторона ав ( а значит и сторона мn потому что сказано что они равны ), а у это сторона аd.

выразим площади  прямоугольников через эти переменные :  

s1 = x * y

s2 = 12*х

сказано что    площадь прямоугольника abcd в 5 раз больше площади прямоугольника mnkl, значит s1 = 5*s2, подставляем :  

х*у = 5*12*х 

х*у = 60*х 

х в обоих частях уравнения уничтожается значит у = 60.

значит ad = 60, посколько ad = bc то и bc = 60.

Воспользуемся  основным тригонометрическим тождество: cos^2(x) + sin^2(x) = 1 интеграл ( dx : (sin(x)*cos(x)) ) = интеграл ( 1*dx : (sin(x)*cos(x)) ) = интеграл ( ( cos^2(x) + sin^2(x) )*dx :   (sin(x)*cos(x)) ) = интеграл ( cos^2(x)*dx: (sin(x)*cos(x)) ) + интеграл ( sin^2(x)*dx :   (sin(x)*cos(x)) ) = интеграл ( cos(x)*dx : sin(x) ) + интеграл ( sin(x)*dx :   cos(x) ) = интеграл ( d(sin(x)) : sin(x) ) + интеграл ( -d(cos(x)) : cos(x) ) = ln (sin(x)) - ln(cos(x)) + c = ln (tg(x)) + c 

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