I3.1 The average of $a, b c$ and $d$ is 8 . If the average of $a, b, c, d$ and $P$ is $P$, find $P$.
13.2 If the lines $2 x+3 y+2=0$ and $P x+Q y+3=0$ are parallel, find $Q$.

I3.3 The perimeter and the area of an equilateral triangle are $Q \mathrm{~cm}$ and $\sqrt{3} R \mathrm{~cm}^{2}$ respectively. Find $R$.

I3.4 If $(1+2+\ldots+R)^{2}=1^{2}+2^{2}+\ldots+R^{2}+S$, find $S$.
$$
\begin{array}{l}
\frac{a+b+c+d}{4}=8 \\
\Rightarrow a+b+c+d=32 \\
\frac{a+b+c+d+P}{5}=P \\
\Rightarrow 32+P=5 P \\
P=8
\end{array}
$$

Their slopes are equal: $-\frac{2}{3}=-\frac{8}{Q}$
$$
Q=12
$$

Perimeter $=12 \mathrm{~cm}$, side $=4 \mathrm{~cm}$
Area $=\frac{1}{2} \cdot 4^{2} \sin 60^{\circ}=4 \sqrt{3}$
$$
\begin{array}{l}
R=4 \\
(1+2+3+4)^{2}=1^{2}+2^{2}+3^{2}+4^{2}+S \\
100=30+S \\
S=70
\end{array}
$$