Questions and Answers
What does x equal if the width of the rectangle is 4x + 2 and the length is x + 4, with a perimeter of 52 ft?
4
What does x equal if the length of a rectangle is x and the width is 4 inches less than 3 times the length, with a perimeter of 32 inches?
5
How long is the length if a rectangular park has a perimeter of 90 ft, with the length as 4x + 1 and width as 6x + 4?
17
What is the width if a rectangle's length is 4 times its width and the perimeter is 80?
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What is the length if a rectangle's length is one more than 4 times its width, with a perimeter of 72?
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What is the width of a rectangle if the width is 3 more than 2 times its length and the perimeter is 54?
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What does x equal if a rectangle has a length of x + 1 and a width of x + 3, with a perimeter of 48?
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What is the length if a rectangle has a length that is 2 more than its width and the perimeter is 40?
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What is the length if a rectangle's length is 1 less than 5 times its width and the perimeter is 34?
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What is the length if a rectangle's width is 2 more than 4 times the length and the perimeter is 114?
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What are the length and width of a rectangle if the length is 4 more meters than its width and the perimeter is 36 meters?
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What are the length and width of a rectangle if the length is 3 times the width and the perimeter is 48 centimeters?
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What are the dimensions of a rectangle if its length is 2 more than 3 times the width and the perimeter is 36 inches?
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What are the lengths of all sides of a triangle with two equal sides and where the third side exceeds the other by 7 feet, given a total perimeter of 25 feet?
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What are the length and width of a rectangle if the length is 4 more inches than its width and the perimeter is 36 inches?
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What are the dimensions of a rectangle if the length is 3 times the width and the perimeter is 48 inches?
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What are the dimensions of a rectangle if the width is six less than the length and the perimeter is 16 inches?
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What are the dimensions of a rectangle if the length is four more than five times the width and the perimeter is 32 inches?
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Study Notes
Perimeter Problems Overview
- The perimeter of a rectangle can be calculated using the formula: Perimeter = 2(Length + Width).
- Different problems present relationships between length and width, often defined in terms of a variable (x).
Specific Problems and Solutions
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Problem 1: Width = 4x + 2, Length = x + 4; Perimeter = 52 ft
- Solution: x = 4
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Problem 2: Length = x, Width = 3x - 4; Perimeter = 32 in
- Solution: x = 5
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Problem 3: Length = 4x + 1, Width = 6x + 4; Perimeter = 90
- Solution: Length = 17
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Problem 4: Length = 4 * Width; Perimeter = 80
- Solution: Width = 8
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Problem 5: Length = 4 * Width + 1; Perimeter = 72
- Solution: Length = 29
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Problem 6: Width = 2 * Length + 3; Perimeter = 54
- Solution: Width = 19
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Problem 7: Length = x + 1, Width = x + 3; Perimeter = 48
- Solution: x = 10
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Problem 8: Length = Width + 2; Perimeter = 40
- Solution: Length = 11
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Problem 9: Length = 5 * Width - 1; Perimeter = 34
- Solution: Length = 14
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Problem 10: Width = 4 * Length + 2; Perimeter = 114
- Solution: Length = 11
Rectangle Dimensions
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Problem 11: Length = Width + 4; Perimeter = 36 m
- Solution: Length = 11 m, Width = 7 m
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Problem 12: Length = 3 * Width; Perimeter = 48 cm
- Solution: Length = 18 cm, Width = 6 cm
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Problem 13: Length = 3 * Width + 2; Perimeter = 36 in
- Solution: Length = 14 in, Width = 4 in
Triangle Perimeter Problem
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Problem 14: Two sides equal, third side = one side + 7 ft; Total Perimeter = 25 ft
- Solution: Side lengths = 6 ft, 6 ft, 13 ft
Additional Equations and Solutions
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Problem 15: Length = Width + 4; Perimeter = 36 in; Equation set with Width = x
- Solution: Width = 7 in, Length = 11 in
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Problem 16: Length = 3 * Width; Perimeter = 48 in; Equation set with Width = x
- Solution: Width = 6 in, Length = 18 in
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Problem 17: Width = Length - 6; Perimeter = 16 in; Equation set with Length = x
- Solution: Length = 7 in, Width = 1 in
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Problem 18: Length = 5 * Width + 4; Perimeter = 32 in; Equation set with Width = x
- Solution: Width = 2 in, Length = 14 in
Key Relationships in Rectangles
- Length and width can be expressed as functions of one another.
- Perimeter provides a constraint to find unknown dimensions.
- Problems designed with variable expressions enhance algebraic understanding.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of perimeter problems in Algebra 1 with these flashcards. Each card presents a different problem involving the dimensions of rectangles and requires you to solve for 'x'. Challenge yourself and improve your algebra skills!
