Answer
The dimension of the rectangular yard: length is $27$ yards and width is $14$ yards.
Work Step by Step
Let the width of the rectangular yard be x, that is,
$W=x$
Then the length of the rectangular yard will be
$\begin{align}
& L=W+13 \\
& =x+13
\end{align}$
The perimeter of the rectangle is given by:
$P=2\left( L+W \right)$
So,
$\begin{align}
& P=2\left( L+W \right) \\
& 82=2\left( x+13+x \right) \\
& 82=2\left( 2x+13 \right) \\
& 82=4x+26
\end{align}$
Further,
$\begin{align}
& 4x=82-26 \\
& 4x=56
\end{align}$
And,
$\begin{align}
& 4x=56 \\
& x=\frac{56}{4} \\
& =14
\end{align}$
Thus, the width of the rectangle yard is $x=14$.
Now we will find the length by substituting $x=14$:
$\begin{align}
& x+13=14+13 \\
& =27
\end{align}$
Hence, the dimension of the rectangular yard is: length is $27$ yards and width is $14$ yards.
