Ques. The perimeter of a rectangle is 26 meters. The difference between the length and the width is 5 meters. Find the width.

The perimeter of a rectangle is 26 meters. The difference between the length and the width is 5 meters. Find the width ?

$$\small{\text{
l=length w=width:
$
\begin{array}{rrcrr}
&2l+2w &=&26\ m & \quad | \quad :2\\
(1)&l+w&=&13\ m \\
(2)&l-w&=&5\ m
\end{array}
$
}}
\\\\
\text{
$\frac{(1)+(2)}{2}=\frac{l+\not{w}+l-\not{w}}{2}=l=\frac{13+5}{2}=9 \ m$
}
\\\\
\text{
$
\frac{(1)-(2)}{2} =\frac{l+w-(l-w)}{2}=\frac{\not{l}+w-\not{l}+w}{2} =w=\frac{13-5}{2}=4\ m
$
}$$