Question

The perimeter of a rectangular field is $82$ m and its area is $400$ $m^2$. Find the breadth of the rectangle.

Answer 1

$\Rightarrow$ Perimeter of rectangular field $=2(l+b)=82m$

$\therefore$ $l+b=41m$

$\Rightarrow$ Let the length of the rectangular field be $xm$, then breadth will be $(41-x)m$

$\Rightarrow$ Area of rectangular field $=l\times b$

$\Rightarrow$ $400=x(41-x)$

$\Rightarrow$ $400=41x-x^2$

$\Rightarrow$ $x^2-41x+400=0$

$\Rightarrow$ $x^2-25x-16x+400=0$

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

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

$\therefore$ $x=25$ and $x=16$

$\therefore$ Length of the rectangle is $25m$ and breadth of the rectangle be $16m$