Answer
$(5$m$)\times(8$m$).$
Work Step by Step
If the sides are x and y, then the area is $xy=40.$
We can express y as $y=\displaystyle \frac{40}{x}$,
because x is not 0.
The perimeter is $\ \ 2x+2y=26$,
into which we substitute $y=\displaystyle \frac{40}{x}$,
$2x+2\displaystyle \cdot\frac{40}{x}=26$
and multiply both sides with x.
$2x^{2}+80=26x$
Divide with 2 and write in standard form
$x^{2}+40=13x$
$x^{2}-13x+40=0$
We can factor the LHS, as -8 and -5 are factors of +40 whose sum is -13....
$(x-5)(x-8)=0$
So, x can be 5 or 8.
If x is 5, then $y=\displaystyle \frac{40}{5}=8$,
and if x =8, then $y=\displaystyle \frac{40}{8}=5.$
Either way, the dimensions of the rectangle are $(5$m$)\times(8$m$).$
