Math Problem Statement
The perimeter of a rectangular field is 380 yd. The length is 30 yd longer than the width. Find the dimensions.
Solution
Let's define the dimensions of the rectangular field.
- Let be the width of the field.
- The length is given as (since the length is 30 yards longer than the width).
The formula for the perimeter of a rectangle is:
We're told the perimeter is 380 yards, so:
Now, let's solve for :
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Distribute the terms:
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Combine like terms:
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Subtract 60 from both sides:
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Divide by 4:
So, the width is 80 yards.
Now, substitute into the expression for the length:
Thus, the dimensions of the field are:
- Width: 80 yards
- Length: 110 yards
Final Answer:
- Width: 80 yards
- Length: 110 yards
Do you want more details or have any questions?
Here are 5 relative questions for further practice:
- What is the area of the field given its dimensions?
- If the perimeter was 500 yards instead, what would the dimensions be?
- How would the dimensions change if the length were twice the width instead of 30 yards longer?
- What is the diagonal length of the field?
- How would the formula for the perimeter change if the field were a square?
Tip: When solving for dimensions in perimeter problems, remember to express both the length and width in terms of one variable before solving.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Linear Equations
Formulas
Perimeter of a rectangle: P = 2l + 2w
Theorems
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Suitable Grade Level
Grades 6-8
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