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Answer :
To solve this problem, we need to find the length and width of a rectangular parking area given some conditions:
1. Understand the Problem:
- The length of the rectangular parking area is two times the width.
- The perimeter of the rectangle is 120 yards.
2. Set Up the Equations:
- Let's denote the width of the rectangle as [tex]\( x \)[/tex].
- Since the length is two times the width, the length will be [tex]\( 2x \)[/tex].
3. Formula for Perimeter:
- The formula for the perimeter of a rectangle is calculated as:
[tex]\[
\text{Perimeter} = 2(\text{Length} + \text{Width})
\][/tex]
- Substituting the expressions for the length and width, we have:
[tex]\[
120 = 2(2x + x)
\][/tex]
4. Simplify and Solve the Equation:
- Simplify inside the parentheses:
[tex]\[
120 = 2(3x) = 6x
\][/tex]
- Solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[
x = \frac{120}{6} = 20
\][/tex]
5. Find Length and Width:
- Now that we have [tex]\( x = 20 \)[/tex], which represents the width,
- Calculate the length as [tex]\( 2x \)[/tex]:
[tex]\[
\text{Length} = 2 \times 20 = 40
\][/tex]
Therefore, the width of the parking area is 20 yards, and the length is 40 yards.
1. Understand the Problem:
- The length of the rectangular parking area is two times the width.
- The perimeter of the rectangle is 120 yards.
2. Set Up the Equations:
- Let's denote the width of the rectangle as [tex]\( x \)[/tex].
- Since the length is two times the width, the length will be [tex]\( 2x \)[/tex].
3. Formula for Perimeter:
- The formula for the perimeter of a rectangle is calculated as:
[tex]\[
\text{Perimeter} = 2(\text{Length} + \text{Width})
\][/tex]
- Substituting the expressions for the length and width, we have:
[tex]\[
120 = 2(2x + x)
\][/tex]
4. Simplify and Solve the Equation:
- Simplify inside the parentheses:
[tex]\[
120 = 2(3x) = 6x
\][/tex]
- Solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[
x = \frac{120}{6} = 20
\][/tex]
5. Find Length and Width:
- Now that we have [tex]\( x = 20 \)[/tex], which represents the width,
- Calculate the length as [tex]\( 2x \)[/tex]:
[tex]\[
\text{Length} = 2 \times 20 = 40
\][/tex]
Therefore, the width of the parking area is 20 yards, and the length is 40 yards.
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