Question

Half the perimeter of a rectangular room is 46 meters and its length is 6 meters more than its width. What is the length and width of the room?

• A. $l=26m,w=20m$
• B. $l=56m,w=40m$
• C. $l=12m,w=9m$
• D. $l=28m,w=18m$

Answer 1

The correct option is A $l=26m,w=20m$

Let $l$ and $w$ be the length and width of the room, respectively.
Then, the perimeter of the room will be $2(l+w)$ m.

Based on the given information,
$l=6+w......\left(1\right)$

$\frac{1}{2}\times 2(l+w)=46$

$\Rightarrow l+w=46......\left(2\right)$

Let's solve these two equations using the substitution method.
Substituting the value of $l$ from equation (1) in equation (2), we get
$\Rightarrow 6+w+w=46$
$\Rightarrow 6+2w=46$
$\Rightarrow 2w=46-6$
$\Rightarrow 2w=40$
$\Rightarrow w=\frac{40}{2}$
$\Rightarrow w=20m$

$l=20+6=26m$

Therefore, the length and width are $26m$ and $20m,$ respectively.