\[\boxed{\text{460\ (460).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ a\ и\ b - катеты\ \]
\[треугольника.\ \]
\[Тогда\ его\ периметр:\ \ \]
\[a + b + 37 = 84.\]
\[По\ теореме\ Пифагора:\]
\[a^{2} + b^{2} = 37^{2}.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} a^{2} + b^{2} = 37^{2}\text{\ \ } \\ a + b + 37 = 84 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (47 - b)^{2} + b^{2} = 37^{2} \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2209 - 94b + b^{2} + b^{2} = 1369 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2b^{2} - 94b + 840 = 0 \\ \end{matrix} \right.\ \]
\[b^{2} - 47b + 420 = 0\]
\[D = 47^{2} - 4 \cdot 420 = 526\]
\[b_{1,2} = \frac{47 \pm 23}{2} = 35;12.\]
\[\left\{ \begin{matrix} b_{1} = 35 \\ a_{1} = 12 \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} b_{2} = 12 \\ a_{2} = 35 \\ \end{matrix} \right.\ ;\ \ \]
\[S = \frac{1}{2} \cdot a \cdot b =\]
\[= \frac{12 \cdot 35}{2} = 210\ \left( см^{2} \right).\]
\[Ответ:210\ см^{2}.\]
\(\boxed{\text{460.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\)
\[\left\{ \begin{matrix} 5x - y - 2 = 0\ \ \ \ \ \ \ \\ x^{2} - 2xy + y^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \\ (x - y)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 5x + 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \ \ \ \ \\ ( - 4x + 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \ \\ (4x - 2)^{2} = 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 5x - 2\ \ \ \ \\ (2x - 1)^{2} = 1 \\ \end{matrix} \right.\ \]
\[2x - 1 = 1\ \ \ \ \ \ \ \ \ 2x - 1 = - 1\]
\[2x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = 0\]
\[x = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 0\]
\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 1 \\ y_{1} = 3 \\ \end{matrix} \right.\ \text{\ \ }или\ \ \ \left\{ \begin{matrix} x_{2} = 0\ \ \ \ \\ y_{2} = - 2. \\ \end{matrix} \right.\ \]
\[Ответ:(1;3);\ \ (0; - 2).\]