#### Answer

The width of the rectangle is $4$ feet and the length is $6$ feet.

#### Work Step by Step

We know that the area of a rectangle is given by the following formula:
$$A = lw$$
where $l$ is the length and $w$ is the width.
We know that the area of this rectangle is $24$ square feet and that the length is two feet greater than its width and can be given by the following equation:
$$l = w + 2$$
We plug this information into the formula for the area of a rectangle to find both length and width:
$$24 = (w + 2)(w)$$
We can use the distributive property to multiply the monomial with each term in the binomial:
$$24 = (w)(w) + (2)(w)$$
Multiply the terms to simplify:
$$24 = w^2 + 2w$$
Subtract $24$ from each side of the equation to make the equation equal to zero. Then we can factor to find the values for $w$:
$$w^2 + 2w - 24 = 0$$
We want to factor this equation so we can use the zero product property to solve for $w$:
To factor, we find the combination of factors for $-24$ that, when added together, equal $2$. Let's examine the factors for $-24$:
$-24$ and $1$ or $24$ and $-1$
$-12$ and $2$ or $12$ and $-2$
$-8$ and $3$ or $8$ and $-3$
$-6$ and $4$ or $6$ and $-4$
It looks like $6$ and $-4$ will work because we need a higher positive number than the negative number. Let's factor the equation using the factors we found:
$$(w + 6)(w - 4) = 0$$
We use the zero product property, which states that the equation equals zero if either of the factors equals zero. So we set each factor equal to zero:
$$w + 6 = 0$$
Subtract $6$ from each side to solve for $w$:
$$w = -6$$
Set the other factor equal to zero:
$$w - 4 = 0$$
Add $4$ to each side of the equation to solve for $w$:
$$w = 4$$
Because measurements cannot be negative, $w$ cannot be $-6$.
If $w = 4$, then we can plug this value in for $w$ into the formula for area to solve for $l$:
$$24 = (l)(4)$$
Divide each side by $4$ to solve for $l$:
$$l = 6$$
The width of the rectangle is $4$ feet and the length is $6$ feet.