G2.2 $E$ is an interior point of the rectangle $A B C D$. Given that the lengths of $E A, E B, E C$ and $E D$ are $2, \sqrt{11}, 4$ and $b$ respectively, find the value of $b$.
$P, Q R, S$ be the foot of perpendiculars drawn from $E$ onto $A B, B C$, $C D, D A$ respectively.
Using Pythagoras' Theorem, it can be proved that
$$
\begin{array}{l}
p^{2}+s^{2}=4 \ldots \ldots \ldots \ldots . .(1) \\
p^{2}+q^{2}=11 \ldots \ldots \ldots . .(2) \\
q^{2}+r^{2}=16 \ldots \ldots \ldots .(3) \\
r^{2}+s^{2}=b^{2} \ldots \ldots \ldots \ldots(4) \\
(1)+(3)-(2)-(4): 0=4+16-11-b^{2} \\
b=3
\end{array}
$$