The perimeter of a rectangular field is 82 m and its area

Let the breadth of the rectangle be $=x$ metres . Then

Perimeter $=82$ metres

2 (length+breadth ) $=82$

(length $+x$ ) $=41$

length $=41-x$

And area of the rectangle

length $\times$ breadth $=400$

$(41-x) x=400$

$41 x-x^{2}=400$

$x^{2}-41 x+400=0$

$x^{2}-25 x-16 x+400=0$

$x(x-25)-16(x-25)=0$

$(x-25)(x-16)=0$

$(x-25)=0$

$x=25$

or

$(x-16)=0$

$x=16$

Since perimeter is 82 meter. So breadth can't be 25 meter.

Hence, breadth 16 metres