The length of a rectangular bedroom is 2 feet more than its width. The area of the bedroom is 120 square feet. Find the length and width of the bedroom.

To find the dimensions of the rectangular bedroom, we need to use the information given:

1. Understanding the problem:
- The length of the bedroom is 2 feet more than the width.
- The area of the bedroom is 120 square feet.
- We need to find both the width and the length.

2. Setting up the equations:
- Let the width be [tex]$ x $[/tex].
- Then, the length can be expressed as [tex]$ x + 2 $[/tex].

3. Using the area formula:
- The area of a rectangle is calculated as length times width.
- So, we set up the equation using this formula:
[tex]\[
x \times (x + 2) = 120
\][/tex]

4. Solving the equation:
- Expand the equation:
[tex]\[
x^2 + 2x = 120
\][/tex]
- Rearrange it into a standard quadratic form:
[tex]\[
x^2 + 2x - 120 = 0
\][/tex]

5. Finding the solution for width [tex]$ x $[/tex]:
- To solve this quadratic equation, we look for values of [tex]$ x $[/tex] that satisfy it. In this case, solving will give two possible solutions where one of them will be positive.
- The positive solution for [tex]$ x $[/tex], which is the width, is 10 feet.

6. Determining the length:
- Once we have the width, the length is:
[tex]\[
x + 2 = 10 + 2 = 12 \text{ feet}
\][/tex]

7. Conclusion:
- Therefore, the width of the bedroom is 10 feet, and the length is 12 feet.