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Answer :
To solve the problem of finding the dimensions of the rectangular bedroom, we can follow these steps:
1. Define the Variables:
- Let the width of the bedroom be denoted by [tex]\( w \)[/tex].
- Since the length is 2 feet more than the width, the length can be expressed as [tex]\( w + 2 \)[/tex].
2. Formulate the Equation:
- The area of a rectangle is given by the product of its length and width.
- Therefore, the equation representing the area is:
[tex]\[
w \times (w + 2) = 120
\][/tex]
3. Solve the Equation:
- First, expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange the equation to set it to zero:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
- This is a quadratic equation, which we can solve for [tex]\( w \)[/tex].
4. Find the Width:
- By solving the quadratic equation, we get two potential solutions: [tex]\(-12\)[/tex] and [tex]\(10\)[/tex].
- Since width cannot be negative, we choose [tex]\( w = 10 \)[/tex].
5. Find the Length:
- Substitute the width value back into the expression for the length:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12
\][/tex]
6. Conclusion:
- The width of the rectangular bedroom is [tex]\( 10 \)[/tex] feet.
- The length of the rectangular bedroom is [tex]\( 12 \)[/tex] feet.
Thus, the dimensions of the bedroom are 10 feet by 12 feet.
1. Define the Variables:
- Let the width of the bedroom be denoted by [tex]\( w \)[/tex].
- Since the length is 2 feet more than the width, the length can be expressed as [tex]\( w + 2 \)[/tex].
2. Formulate the Equation:
- The area of a rectangle is given by the product of its length and width.
- Therefore, the equation representing the area is:
[tex]\[
w \times (w + 2) = 120
\][/tex]
3. Solve the Equation:
- First, expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange the equation to set it to zero:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
- This is a quadratic equation, which we can solve for [tex]\( w \)[/tex].
4. Find the Width:
- By solving the quadratic equation, we get two potential solutions: [tex]\(-12\)[/tex] and [tex]\(10\)[/tex].
- Since width cannot be negative, we choose [tex]\( w = 10 \)[/tex].
5. Find the Length:
- Substitute the width value back into the expression for the length:
[tex]\[
\text{Length} = w + 2 = 10 + 2 = 12
\][/tex]
6. Conclusion:
- The width of the rectangular bedroom is [tex]\( 10 \)[/tex] feet.
- The length of the rectangular bedroom is [tex]\( 12 \)[/tex] feet.
Thus, the dimensions of the bedroom are 10 feet by 12 feet.
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