SenorMathWiz
Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice's fence if the area of her garden s 5,670 square feet?

Sagot :

Space

Answer:

P = 342 ft

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. 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

  1. Substitute in variables [Area of a Rectangle Formula]:                                w(3w - 9) = 5670
  2. [Distributive Property] Expand:                                                                      3w² - 9w = 5670
  3. [Subtraction Property of Equality] Rewrite [Standard Form]:                      3w² - 9w - 5670 = 0
  4. [Quadratic] Factor:                                                                                          3(w - 45)(w + 42) = 0
  5. [Quadratic] Solve [Find roots]:                                                                      w = -42, 45

Since length/width cannot be negative, we know that w = 45 ft.

Step 3: Find l

  1. Substitute in w [Length Formula]:                                                                   l = 3(45) - 9
  2. [Order of Operations] Evaluate:                                                                       l = 126 ft

Step 4: Find Perimeter

  1. Substitute in variables [Perimeter of a Rectangle Formula]:                        P = 2(45 ft) + 2(126 ft)
  2. [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
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.