Answer
Length: 8 meters
Width: 5 meters
Work Step by Step
Let's note:
$l$=the length of the rectangle
$w$=the width of the rectangle
We can write the system:
$\begin{cases}
2l+2w=26\\
lw=40
\end{cases}$
$\begin{cases}
l+w=13\\
lw=40
\end{cases}$
We will use the substitution method. Solve Equation 1 for $l$ and substitute the expression of $l$ in Equation 2 to eliminate $l$ and determine $w$:
$\begin{cases}
l=13-w\\
(13-w)w=40
\end{cases}$
$13w-w^2=40$
$w^2-13w+40=0$
$w^2-5w-8w+40=0$
$w(w-5)-8(w-5)=0$
$(w-5)(w-8)=0$
$w-5=0\Rightarrow w_1=5$
$w-8=0\Rightarrow w_2=8$
Substitute each of the values of $w$ in the expression of $l$ to determine $l$:
$l=13-w$
$w_1=5\Rightarrow l_1=13-5=8$
$w_2=8\Rightarrow l_2=13-8=5$
The system's solutions are:
$(8,5), (5,8)$
As the length is greater or equal to the width, the solution is:
$l=8$
$w=5$
