Đáp án: $a = \sqrt {37} $
Giải thích các bước giải:
$\begin{array}{l}
p = \frac{{a + b + c}}{2} = \frac{{a + 3 + 4}}{2} = \frac{a}{2} + \frac{7}{2}\\
S = \sqrt {p\left( {p - a} \right)\left( {p - b} \right).\left( {p - c} \right)} \\
\Rightarrow {S^2} = p.\left( {p - a} \right).\left( {p - 4} \right).\left( {p - 3} \right)\\
\Rightarrow 27 = \frac{{a + 7}}{2}.\left( {\frac{{a + 7}}{2} - a} \right).\left( {\frac{{a + 7}}{2} - 4} \right).\left( {\frac{{a + 7}}{2} - 3} \right)\\
\Rightarrow 27 = \frac{{a + 7}}{2}.\frac{{7 - a}}{2}.\frac{{a - 1}}{2}.\frac{{a + 1}}{2}\\
\Rightarrow {27.4^2} = \left( {49 - {a^2}} \right).\left( {{a^2} - 1} \right)\\
\Rightarrow a = \sqrt {37}
\end{array}$
