G9.1 The area of an equilateral triangle is $50 \sqrt{12}$. If its perimeter is $p$, find $p$.
G9.2 The average of $q, y, z$ is 14 . The average of $q, y, z, t$ is 13 . Find $t$.
G9.3 If $7-24 x-4 x^{2} \equiv K+A(x+B)^{2}$, where $K, A, B$ are constants, find $K$.
G9.4 If $C=\frac{3^{4 n} \cdot 9^{n+4}}{27^{2 n+2}}$, find $C$.
$\begin{array}{l}\text { Each side }=\frac{p}{3} \\ \frac{1}{2} \cdot\left(\frac{p}{3}\right)^{2} \sin 60^{\circ}=50 \sqrt{12}=100 \sqrt{3} \\ p=60 \\ \frac{q+y+z}{3}=14 \\ \Rightarrow q+y+z=42 \\ \frac{q+y+z+t}{4}=13 \\ \Rightarrow \frac{42+t}{4}=13 \\ t=10 \\ 7-24 x-4 x^{2} \equiv-4\left(x^{2}+6 x\right)+7 \equiv-4(x+3)^{2}+43 \\ K=43 \\ C=\frac{3^{4 n} \cdot 3^{2 n+8}}{3^{6 n+6}}=9 \\\end{array}$