Answer
The length of the rectangle is $15\text{m}$ and the width is $4.9\text{m}$.
Work Step by Step
Suppose the width of the rectangle is $b=x$, then the length of the rectangle is $l=x+10.1$.
The perimeter of the rectangle is $P=2\left( l+b \right)$; therefore,
$\begin{align}
& P=2\left( l+b \right) \\
& 39.8=2\left( x+10.1+x \right) \\
& 39.8=2\left( 2x+10.1 \right) \\
& 39.8=4x+20.2
\end{align}$
Further simplify:
$\begin{align}
& 39.8-20.2=4x \\
& 4x=19.6 \\
& x=\frac{19.6}{4} \\
& x=4.9
\end{align}$
Therefore, the width of the rectangle is $x=4.9$ and the length will be,
$\begin{align}
& l=x+10.1 \\
& =4.9+10.1 \\
& =15.0
\end{align}$
Hence, the length of the rectangle is $\text{15m}$ and the width is $\text{4}\text{.9m}$.
