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Answer :
To find the length and width of the rectangular bedroom, let's work through the problem step-by-step.
1. Understand the problem:
- We are told that the bedroom is rectangular, and its area is 120 square feet.
- The length of the bedroom is 2 feet more than its width.
2. Set up the variables:
- Let [tex]\( w \)[/tex] be the width of the bedroom.
- Therefore, the length [tex]\( l \)[/tex] would be [tex]\( w + 2 \)[/tex].
3. Write the equation for the area:
- The area of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Substituting the given values, we have:
[tex]\[
(w + 2) \times w = 120
\][/tex]
4. Solve the equation:
- Expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange it into standard quadratic form:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
5. Solve the quadratic equation:
- Factor or use the quadratic formula to find the value of [tex]\( w \)[/tex].
- The quadratic formula is:
[tex]\[
w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\][/tex]
- In this equation, [tex]\( a = 1 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = -120 \)[/tex].
- Solving this equation, the positive solution is [tex]\( w = 10 \)[/tex].
- (We discard the negative solution, as widths cannot be negative.)
6. Find the length:
- Since the length [tex]\( l \)[/tex] is [tex]\( w + 2 \)[/tex]:
[tex]\[
l = 10 + 2 = 12
\][/tex]
7. Conclusion:
- The width of the bedroom is 10 feet, and the length is 12 feet.
So, the dimensions of the bedroom are a width of 10 feet and a length of 12 feet.
1. Understand the problem:
- We are told that the bedroom is rectangular, and its area is 120 square feet.
- The length of the bedroom is 2 feet more than its width.
2. Set up the variables:
- Let [tex]\( w \)[/tex] be the width of the bedroom.
- Therefore, the length [tex]\( l \)[/tex] would be [tex]\( w + 2 \)[/tex].
3. Write the equation for the area:
- The area of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Substituting the given values, we have:
[tex]\[
(w + 2) \times w = 120
\][/tex]
4. Solve the equation:
- Expand the equation:
[tex]\[
w^2 + 2w = 120
\][/tex]
- Rearrange it into standard quadratic form:
[tex]\[
w^2 + 2w - 120 = 0
\][/tex]
5. Solve the quadratic equation:
- Factor or use the quadratic formula to find the value of [tex]\( w \)[/tex].
- The quadratic formula is:
[tex]\[
w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\][/tex]
- In this equation, [tex]\( a = 1 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = -120 \)[/tex].
- Solving this equation, the positive solution is [tex]\( w = 10 \)[/tex].
- (We discard the negative solution, as widths cannot be negative.)
6. Find the length:
- Since the length [tex]\( l \)[/tex] is [tex]\( w + 2 \)[/tex]:
[tex]\[
l = 10 + 2 = 12
\][/tex]
7. Conclusion:
- The width of the bedroom is 10 feet, and the length is 12 feet.
So, the dimensions of the bedroom are a width of 10 feet and a length of 12 feet.
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