Let l be the length of the rectangle, then we can set the following equation:
[tex]l=2w-5m\text{.}[/tex]Where w is the width of the rectangle. Now, the formula for the area of a rectangle is:
[tex]A=lw\text{.}[/tex]Solving the above equation for l, we get:
[tex]l=\frac{A}{w}\text{.}[/tex]Substituting l=A/w in the first equation we get:
[tex]\frac{A}{w}=2w-5m\text{.}[/tex]Solving for w, and considering that A=52 m²we get:
[tex]\begin{gathered} A=(2w-5m)w, \\ A=2w^2-(5m)w, \\ 52m^2=2w^2-(5m)w, \\ 2w^2-(5m)w-52m^2=0, \\ (2w-13m)(w+4m)=0, \\ w=\frac{13}{2}m\text{.} \end{gathered}[/tex]Substituting w=4m in the first equation we get:
[tex]l=13m-5m=8m\text{.}[/tex]Answer:
Length: 8 m,
Width: 6.5 m.
