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Answer :
To find the length and width of the rectangular bedroom, we can follow these steps:
1. Understand the Relationship:
- Let's denote the width of the bedroom as [tex]\( w \)[/tex].
- The length of the bedroom is 2 feet more than its width, so we can express the length as [tex]\( w + 2 \)[/tex].
2. Area Equation:
- The area of a rectangle is calculated as [tex]\( \text{length} \times \text{width} \)[/tex].
- Given that the area is 120 square feet, we can set up the equation:
[tex]\[
(w + 2) \times w = 120
\][/tex]
3. Form a Quadratic Equation:
- Expand the equation:
[tex]\[
w(w + 2) = 120
\][/tex]
- This simplifies to:
[tex]\[
w^2 + 2w = 120
\][/tex]
- To make it a standard quadratic equation, move 120 to the other side:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
4. Solve the Quadratic Equation:
- The quadratic equation is [tex]\( w^2 + 2w - 120 = 0 \)[/tex].
- Solving this equation gives us the value(s) for [tex]\( w \)[/tex].
5. Find the Positive Solution:
- Since width cannot be negative, we consider only the positive solution.
- The possible value for width that satisfies the equation is 10 feet.
6. Calculate the Length:
- Since the length is 2 feet more than the width:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12 \text{ feet}
\][/tex]
Therefore, the width of the bedroom is 10 feet, and the length is 12 feet.
1. Understand the Relationship:
- Let's denote the width of the bedroom as [tex]\( w \)[/tex].
- The length of the bedroom is 2 feet more than its width, so we can express the length as [tex]\( w + 2 \)[/tex].
2. Area Equation:
- The area of a rectangle is calculated as [tex]\( \text{length} \times \text{width} \)[/tex].
- Given that the area is 120 square feet, we can set up the equation:
[tex]\[
(w + 2) \times w = 120
\][/tex]
3. Form a Quadratic Equation:
- Expand the equation:
[tex]\[
w(w + 2) = 120
\][/tex]
- This simplifies to:
[tex]\[
w^2 + 2w = 120
\][/tex]
- To make it a standard quadratic equation, move 120 to the other side:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
4. Solve the Quadratic Equation:
- The quadratic equation is [tex]\( w^2 + 2w - 120 = 0 \)[/tex].
- Solving this equation gives us the value(s) for [tex]\( w \)[/tex].
5. Find the Positive Solution:
- Since width cannot be negative, we consider only the positive solution.
- The possible value for width that satisfies the equation is 10 feet.
6. Calculate the Length:
- Since the length is 2 feet more than the width:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12 \text{ feet}
\][/tex]
Therefore, the width of the bedroom is 10 feet, and the length is 12 feet.
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