Question

The area of a rectangle is $192$ cm${}^2$ and its perimeter is $56$ cm. Find the length

Answer 1

Let the length of the rectangle $=l$ cm and breadth $=b$ cm.
Area of the rectangle $=l\times b=192{cm}^2$ ....(1)
Perimeter of the rectangle $=2(l+b)=56$ cm

$\Rightarrow l+b=28$ or $l=28-b$ ....(2)
Putting the value of $l$ in equation (1), we get
$(28-b)\times b=192$
$28b-b^2=192$
$b^2-28b+192=0$
$(b-16)(b-12)=0$
$=>b=16$ or $12$ cm
Substituting the value of $b$ $=16$ cm in equation (1), we get

$l\times 16=192$

$\Rightarrow l=12$ cm
Similarly, if $b$ $=12$ cm, $l=16$ cm.
Dimension of the rectangle are $12$ cm and $16$ cm.