\(
\begin{array}{l}
\left\{ \begin{array}{l}
L + W = 150 \\
L \cdot W = 4400 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
L + W = 150 \\
L = \frac{{4400}}{W} \\
\end{array} \right. \\
\left\{ \begin{array}{l}
\frac{{4400}}{W} + W = 150 \\
L = \frac{{4400}}{W} \\
\end{array} \right. \\
\left\{ \begin{array}{l}
4400 + W^2 = 150W \\
L = \frac{{4400}}{W} \\
\end{array} \right. \\
\left\{ \begin{array}{l}
W^2 - 150W + 4400 = 0 \\
L = \frac{{4400}}{W} \\
\end{array} \right. \\
W^2 - 150W + 4400 = 0 \\
(W - 75)^2 - 5625 + 4400 = 0 \\
(W - 75)^2 - 1225 = 0 \\
(W - 75)^2 = 1225 \\
W - 75 = \pm 35 \\
W = 40 \vee W = 110 \\
\end{array}
\)
