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Sagot :
Answer:
P = 342 ft
General Formulas and Concepts:
Pre-Algebra
Evaluations
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Distributive Property
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Terms/Coefficients
- Factoring/Expanding
Quadratics
- Solving quadratic equations
- Standard Form: ax² + bx + c = 0
Geometry
Area of a Rectangle Formula: A = lw
- l is length
- w is width
Perimeter of a Rectangle Formula: P = 2w + 2l
- l is length
- w is width
Step-by-step explanation:
Step 1: Define
Identify variables.
A = 5670 ft²
"Length that is 9 feet less than 3 times its width" → l = 3w - 9
Step 2: Find w
- Substitute in variables [Area of a Rectangle Formula]: w(3w - 9) = 5670
- [Distributive Property] Expand: 3w² - 9w = 5670
- [Subtraction Property of Equality] Rewrite [Standard Form]: 3w² - 9w - 5670 = 0
- [Quadratic] Factor: 3(w - 45)(w + 42) = 0
- [Quadratic] Solve [Find roots]: w = -42, 45
Since length/width cannot be negative, we know that w = 45 ft.
Step 3: Find l
- Substitute in w [Length Formula]: l = 3(45) - 9
- [Order of Operations] Evaluate: l = 126 ft
Step 4: Find Perimeter
- Substitute in variables [Perimeter of a Rectangle Formula]: P = 2(45 ft) + 2(126 ft)
- [Order of Operations] Evaluate: P = 342 ft
∴ The perimeter of Janice's fence is 342 ft.
Let width be x ft
Length be 3x-9ft
Now
- Area=Length ×Breadth
- 5670=x(3x-9)
- 5670=3x²-9x
- 3x²-9x-5670=0
On solving we wI'll get x=-42,45
Take it positive
- x=45
- width=45ft
- Length=3(45)-9=135-9=126ft
Now
Perimeter
- 2(Length+Width)
- 2(45+126)
- 2(171)
- 342ft
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