Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
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
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.