College

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.

Answer :

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.