Đáp án:
Kẻ BH vuông góc với AC
=> AH = AC - CH = 7-CH
Áp dụng Pytago trong tam giác vuông tại H ta có:
$\begin{array}{l}
\left\{ \begin{array}{l}
A{B^2} = B{H^2} + A{H^2}\\
B{C^2} = B{H^2} + C{H^2}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
{8^2} = B{H^2} + {\left( {7 - CH} \right)^2}\\
{10^2} = B{H^2} + C{H^2}
\end{array} \right.\\
\Rightarrow {8^2} - {\left( {7 - CH} \right)^2} = {10^2} - C{H^2}\\
\Rightarrow 64 - 49 + 14CH - C{H^2} = 100 - C{H^2}\\
\Rightarrow 14CH = 85\\
\Rightarrow CH = \dfrac{{85}}{{14}}\left( {cm} \right)\\
\Rightarrow B{H^2} = {10^2} - C{H^2} = \dfrac{{12375}}{{196}}\\
Do:CH = CD + DH\\
\Rightarrow DH = \dfrac{{85}}{{14}} - 6 = \dfrac{1}{{14}}\left( {cm} \right)\\
Trong:\Delta BDH \bot H\\
\Rightarrow B{D^2} = B{H^2} + D{H^2}\\
= \dfrac{{442}}{7}\\
\Rightarrow BD = \dfrac{{\sqrt {3094} }}{7}\left( {cm} \right)
\end{array}$
