Answer :
Sure! Let's find the length and width of the rectangular bedroom step-by-step.
1. Define the Variables:
- Let the width of the bedroom be [tex]\( w \)[/tex] feet.
- Since the length is 2 feet more than the width, the length can be expressed as [tex]\( w + 2 \)[/tex].
2. Use the Area Formula:
- The area of a rectangle is given by multiplying its length by its width. Therefore, we have:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Based on the information given, the equation becomes:
[tex]\[
(w + 2) \times w = 120
\][/tex]
3. Form a Quadratic Equation:
- Expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange to form a quadratic equation:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
4. Solve the Quadratic Equation:
- To find the values of [tex]\( w \)[/tex], we solve the equation [tex]\( w^2 + 2w - 120 = 0 \)[/tex].
- The solutions to this equation are [tex]\( w = -12 \)[/tex] and [tex]\( w = 10 \)[/tex].
5. Choose the Logical Solution:
- Since width cannot be negative, we take [tex]\( w = 10 \)[/tex].
6. Calculate the Length:
- The length of the bedroom is 2 feet more than its width:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12 \text{ feet}
\][/tex]
Thus, the width of the bedroom is 10 feet, and the length is 12 feet.
1. Define the Variables:
- Let the width of the bedroom be [tex]\( w \)[/tex] feet.
- Since the length is 2 feet more than the width, the length can be expressed as [tex]\( w + 2 \)[/tex].
2. Use the Area Formula:
- The area of a rectangle is given by multiplying its length by its width. Therefore, we have:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Based on the information given, the equation becomes:
[tex]\[
(w + 2) \times w = 120
\][/tex]
3. Form a Quadratic Equation:
- Expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange to form a quadratic equation:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
4. Solve the Quadratic Equation:
- To find the values of [tex]\( w \)[/tex], we solve the equation [tex]\( w^2 + 2w - 120 = 0 \)[/tex].
- The solutions to this equation are [tex]\( w = -12 \)[/tex] and [tex]\( w = 10 \)[/tex].
5. Choose the Logical Solution:
- Since width cannot be negative, we take [tex]\( w = 10 \)[/tex].
6. Calculate the Length:
- The length of the bedroom is 2 feet more than its width:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12 \text{ feet}
\][/tex]
Thus, the width of the bedroom is 10 feet, and the length is 12 feet.
