#### Answer

$b=3\ ,l=\ 8$.

#### Work Step by Step

We have the formula for the perimeter:
$P=2\left( l+b \right)$
So
$\begin{align}
& 22=2\left( l+b \right) \\
& 11=l+b \\
& l=11-b
\end{align}$
The area is $A=l\times b$ ,
So, $24=l\times b$
Substituting the value of the length in equation $24=l\times b$, we get
${{b}^{2}}-11b+24=0$
On solving the above quadratic equation, we get $b=3\text{ and}\ 8$.
Substituting $b$ in equation $l=11-b$. When $b=3$ the value of $l=8$ and when $b=8$ the value of $l=3$.