The length of a rectangle is one unit more than its width. If the area is 30 square units, find the dimensions of the rectangle.

A = LW

30 = 6 * 5

To find the dimensions of the rectangle, we can use the formula for the area of a rectangle, which is length multiplied by width.

Let's call the width of the rectangle 'w' units.
According to the problem, the length is one unit more than the width, so the length would be 'w + 1' units.

The area of the rectangle is given as 30 square units. We can now set up the equation:

Area = Length × Width
30 = (w + 1) × w

Expanding the equation:
30 = w^2 + w

Rearranging the equation and setting it equal to zero:
w^2 + w - 30 = 0

Now we can solve this quadratic equation either by factoring or by using the quadratic formula.

Factoring:
(w + 6)(w - 5) = 0

Setting each factor equal to zero:
w + 6 = 0 or w - 5 = 0

Solving for 'w':
w = -6 or w = 5

Since the width cannot be negative, we disregard w = -6.

Therefore, the width of the rectangle is 5 units.

Now, we can find the length by adding 1 to the width:
Length = Width + 1
Length = 5 + 1
Length = 6 units

So, the dimensions of the rectangle are: Width = 5 units and Length = 6 units.

To find the dimensions of the rectangle, we need to set up an equation based on the given information.

Let's assume that the width of the rectangle is x units.

According to the given information, the length of the rectangle is one unit more than its width. Therefore, the length of the rectangle would be x + 1 units.

The area of a rectangle is found by multiplying its length (x + 1) by its width (x). So, we have the equation:

Area = Length × Width
30 = (x + 1) × x

Now we can solve this equation to find the dimensions of the rectangle.

Expanding the equation:
30 = x² + x

Rearranging the equation:
x² + x - 30 = 0

Now we can factorize or use the quadratic formula to solve for x. Let's use factoring:

(x + 6)(x - 5) = 0

To find the possible values for x, we set each factor to zero:

x + 6 = 0 or x - 5 = 0

Solving for x, we get:
x = -6 or x = 5

Since the width of a rectangle cannot be negative, we can discard x = -6. So, the width of the rectangle is x = 5 units.

Now we can find the length by adding 1 to the width:
Length = Width + 1
Length = 5 + 1
Length = 6 units

Therefore, the dimensions of the rectangle are width = 5 units and length = 6 units.