Đáp án:
b) ${S_{ABC}} = \dfrac{{29}}{2}$
c) ${P_{ABC}} = 2\sqrt {29} + \sqrt {58}$
Giải thích các bước giải:
\(\begin{array}{l}
\overrightarrow {AB} = \left( {5;2} \right);\,\overrightarrow {AC} = \left( {3;7} \right);\,\overrightarrow {BC} = \left( { - 2;5} \right)\\
a) \Rightarrow AB = BC = \sqrt {29} ;AC = \sqrt {58} ;\,\overrightarrow {AB} .\overrightarrow {BC} = 5.\left( { - 2} \right) + 2.5 = 0\\
\Rightarrow AB \bot BC\\
\Rightarrow \Delta ABC\,vuong\,can\,tai\,B\\
b){S_{ABC}} = \dfrac{1}{2}AB.BC = \dfrac{{29}}{2}\\
BH \bot AC \Rightarrow H\,la\,trung\,diem\,AC\\
BH = \dfrac{{AC}}{2} = \dfrac{{\sqrt {58} }}{2}\\
c)\,{P_{ABC}} = AB + AC + BC = 2\sqrt {29} + \sqrt {58} \\
BK = \dfrac{{AC}}{2} = \dfrac{{\sqrt {58} }}{2}\,
\end{array}\)