Question

The length of a rectangular field is $8meters$ less than twice its breadth. If the perimeter of the rectangular field is $56metres$, find the length of its sides.

Answer 1

Let length and breadth the field are $l$ and $b$ respectively. Then,

$l=2b-8$
$\Rightarrow 2b=8+l\cdots \left(1\right)$

The perimeter of the rectangular field $=56$ m

$\Rightarrow 2(l+b)=56m$
$\Rightarrow 2l+2b=56m$

From $\left(1\right)$, we get

$2l+8+l=56$
$\Rightarrow 3l=56-8$
$\Rightarrow 3l=48$
$\Rightarrow l=\frac{48}{3}$
$\Rightarrow l=16m$

$\therefore$ Length of rectangular field $=16m$
Lets substitute the value of $l=16$ in $\left(1\right)$,
$2b=8+16=24$
$\Rightarrow b=\frac{24}{2}$
$\Rightarrow b=12$

$\therefore$ Breadth of rectangular field $=12m$
Therefore, length of rectangular sides is $16m$ and $12m$ respectively.