Question

Сделайте двенадцатое(12) в самом низу

Answer 1

$\Delta NMC \sim \Delta FER$

По подобию треугольников:

$\frac{NC}{FR} = \frac{MC}{ER} = \frac{NM}{FE} = \frac{7}{6}$

$\angle NMC = \angle FER$

$S_{\Delta NMC} = \frac{1}{2}\cdot NM\cdot MC\cdot\sin(\angle NMC)$

$S_{\Delta FER} = \frac{1}{2}\cdot FE\cdot ER\cdot\sin(\angle FER)$

$\frac{S_{\Delta NMC}}{S_{\Delta FER}} = \frac{y}{x}$

$\frac{S_{\Delta NMC}}{S_{\Delta FER}} = \frac{0{,}5\cdot NM\cdot MC\cdot\sin(\angle NMC)}{0{,}5\cdot FE\cdot ER\cdot\sin(\angle FER)} =$

$= \frac{NM}{FE}\cdot\frac{MC}{ER} = \frac{7}{6}\cdot\frac{7}{6} =$

$= \frac{49}{36}$

$\frac{y}{x} = \frac{49}{36}$

$26 = S_{\Delta MNC} - S_{\Delta FER} = y - x$

$y = x + 26$

$\frac{x+26}{x} = \frac{49}{36}$

$36\cdot (x+26) = 49\cdot x$

$36x + 36\cdot 26 = 49x$

$49x - 36x = 36\cdot 26$

$13x = 36\cdot 26$

$x = \frac{36\cdot 26}{13} = 36\cdot 2 = 72$

$y = x + 26 = 72 + 26 = 98$