Đáp án:
\(Vay\,\,\,\Delta ABC\,\,co:\,\,\,AB = 33,\,\,AC = 44,\,\,BC = 55\,\,\,hoac\,\,\,AB = 44,\,\,AC = 33,\,\,\,BC = 55.\)
Giải thích các bước giải:
\(\begin{array}{l}
Ta\,\,co:\,\,\,AB + BC + CA = 132\\
Ap\,\,dung\,\,dinh\,\,ly\,\,Pitago\,\,\,ta\,\,co:\,\,\,B{C^2} = A{B^2} + A{C^2}\\
Theo\,\,\,de\,\,bai\,\,ta\,\,co:\,\,A{B^2} + A{C^2} + B{C^2} = 6050\\
\Rightarrow 2B{C^2} = 6050\\
\Leftrightarrow B{C^2} = 3025\\
\Leftrightarrow BC = 55.\\
\Rightarrow \left\{ \begin{array}{l}
AB + AC = 132 - BC = 77\\
A{B^2} + A{C^2} = {55^2}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
AB = 77 - AC\\
{\left( {77 - AC} \right)^2} + A{C^2} = {55^2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
AB = 77 - AC\\
5929 - 154AC + 2A{C^2} = 3025
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
AB = 77 - AC\\
2A{C^2} - 154AC + 2904 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
AB = 77 - AC\\
\left[ \begin{array}{l}
AC = 44\\
AC = 33
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
AB = 33\\
AC = 44
\end{array} \right.\\
\left\{ \begin{array}{l}
AB = 44\\
AC = 33
\end{array} \right.
\end{array} \right..\\
Vay\,\,\,\Delta ABC\,\,co:\,\,\,AB = 33,\,\,AC = 44,\,\,BC = 55\,\,\,hoac\,\,\,AB = 44,\,\,AC = 33,\,\,\,BC = 55.
\end{array}\)
