#### Answer

The width is 6
The length is 11

#### Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$
Then we can factor the trinomial as follows:
$~x^2+bx+c = (x+r)~(x+s)$
We can rearrange the given equation:
$w~(w+5)=66$
$w^2+5w=66$
$w^2+5w-66 = 0$
To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -66$. We can see that $(11)+(-6) = 5~$ and $(11)\times (-6) = -66$
We can solve the equation as follows:
$w~(w+5)=66$
$w^2+5w=66$
$w^2+5w-66 = 0$
$(w+11)~(w-6) = 0$
$w+11 = 0~~$ or $~~w-6 = 0$
$w = -11~~$ or $~~w = 6$
Since the width must be a positive number, $w = 6$
We can find the length:
$w+5 = 6+5 = 11$