Đáp án:
Theo hệ thức lượng ta có:
$\begin{array}{l}
A{H^2} = HB.HC\\
\Rightarrow HB.HC = 36\\
Do:HC - HB = 3,5\\
\Rightarrow HC = HB + 3,5\\
\Rightarrow HB.\left( {HB + 3,5} \right) = 36\\
\Rightarrow H{B^2} + 3,5HB - 36 = 0\\
\Rightarrow \left( {HB + 8} \right)\left( {HB - 4,5} \right) = 0\\
\Rightarrow HB = 4,5\left( {cm} \right)\left( {Do:HB > 0} \right)\\
\Rightarrow HC = HB + 3,5 = 8\left( {cm} \right)\\
\Rightarrow \left\{ \begin{array}{l}
AB = \sqrt {A{H^2} + H{B^2}} = 7,5\left( {cm} \right)\\
AC = \sqrt {A{H^2} + H{C^2}} = 10\left( {cm} \right)
\end{array} \right.
\end{array}$
