\((1)\)等比数列\(\{a_{n}\}\)中,\(a_{1}=2\),\(a_{5}=8\),则\(a_{3}=\)__________.
\((2)\)曲线\(f(x)=x\ln x\)在点\(P(1,0)\)处的切线\(l\)与两坐标轴围成的三角形的面积是__________.
\((3)\)已知实数\(x\)、\(y\)满足不等式组\(\begin{cases}\begin{matrix}x\leqslant 1 \\ x-y+{m}^{2}\geqslant 0\end{matrix} \\ x+y-1\geqslant 0\end{cases} \)若目标函数\(z=-2x+y\)的最大值不超过\(4\),则实数\(m\)的取值范围是__________.
\((4)\)已知点\(P\)是双曲线\(\dfrac{{{x}^{2}}}{a}-\dfrac{{{y}^{2}}}{3a}=1(a > 0)\)右支上任意一点,由\(P\)点向两条渐近线引垂线,垂足分别为\(E\)、\(F\),若\(\triangle PEF\)的面积为\(\dfrac{{3}\sqrt{{3}}}{{8}}\),则\(a\)的值为__________.