The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units. What is the width, in units, of the rectangle?

Let L be the length then the width is (L-3) and we know area is L(W)

So
Area = (L)(L-3)
and Area is
28 so
28=(L)(L-3)
use the distributive property then move your equation to the right hand side and solve for the roots : )
Hint the factors of the quadratic are 7 and 4, you figure out the signs : )

To find the width of the rectangle, we first need to set up an equation using the given information. Let's denote the length of the rectangle as "L" and the width as "W".

According to the problem, the width is 3 units less than the length, so we can write this as:

W = L - 3

The area of a rectangle is given by the formula A = Length * Width. In this case, the area is 28 units, so we can write:

28 = L * W

Now, substitute the value of W from the first equation into the second equation:

28 = L * (L - 3)

Simplify the equation:

28 = L^2 - 3L

Rearrange the equation to get it into quadratic form:

L^2 - 3L - 28 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

Factoring this quadratic equation, we find:

(L - 7)(L + 4) = 0

Setting each factor equal to zero:

L - 7 = 0 or L + 4 = 0

Solving for L, we get:

L = 7 or L = -4

Since the length of a rectangle cannot be negative, we discard the negative solution.

Therefore, the length of the rectangle is L = 7 units.

Now, substitute this value back into the first equation to find the width:

W = L - 3
W = 7 - 3
W = 4

Therefore, the width of the rectangle is 4 units.