The length of a rectangle is 4 inches more than twice the width. If the area of the rectangle is 48 square inches, what is the length of the rectangle? SHOW WORK.

Thank you!!

w(2w+4) = 48

w(w+2) = 24

4*6 = 24
4*12 = 48

or, you can solve the quadratic.

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

According to the problem, the length of the rectangle is 4 inches more than twice the width. So, the length can be derived as:
Length = 2 * Width + 4
Length = 2x + 4

The formula to find the area of a rectangle is:
Area = Length * Width

Substituting the given values, we have:
48 = (2x + 4) * x

Now, let's solve for x by simplifying the equation and bringing all the terms to one side:
48 = 2x^2 + 4x

Rearranging the equation, we get:
2x^2 + 4x - 48 = 0

Now, let's factorize or solve this quadratic equation to find the values of x:
2(x^2 + 2x - 24) = 0

Factoring the equation, we get:
2(x + 6)(x - 4) = 0

Setting each factor to zero, we have:
x + 6 = 0 or x - 4 = 0

Solving for x, we get:
x = -6 or x = 4

Since the width of a rectangle cannot be negative, we ignore the solution x = -6. Hence, the width of the rectangle is 4 inches.

Now, substituting the value of x in the length equation, we get:
Length = 2x + 4 = 2 * 4 + 4 = 8 + 4 = 12

Therefore, the length of the rectangle is 12 inches.

To find the length of the rectangle, we can set up an equation based on the given information.

Let's say the width of the rectangle is represented by "w" inches. According to the problem, the length is 4 inches more than twice the width, which can be represented as: 2w + 4.

The formula for the area of a rectangle is length multiplied by width:

Area = length * width

Using the given information that the area is 48 square inches, we can substitute the values into the equation:

48 = (2w + 4) * w

Expanding the equation:
48 = 2w^2 + 4w

Rearranging the equation to make it a quadratic equation:
2w^2 + 4w - 48 = 0

Now we can solve this quadratic equation. You can solve it by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring in this case:

2w^2 + 4w - 48 = 0

Dividing the equation by 2 to simplify:
w^2 + 2w - 24 = 0

Next, we need to find two numbers that multiply to -24 and add up to 2. In this case, the numbers are 6 and -4:
(w + 6)(w - 4) = 0

Setting each factor equal to zero:
w + 6 = 0 or w - 4 = 0

Solving for w:
w = -6 or w = 4

Since the width cannot be a negative value in this context, we discard the solution w = -6.

Therefore, the width of the rectangle is 4 inches.

Now, let's find the length using the formula we obtained earlier:
length = 2w + 4
length = 2(4) + 4
length = 8 + 4
length = 12

Therefore, the length of the rectangle is 12 inches.

To summarize:
- The width of the rectangle is 4 inches.
- The length of the rectangle is 12 inches.