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gizmo_the_mogwai [7]
2 years ago
10

A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expre

ssion represents the perimeter, in centimeters, of the triangle?
Mathematics
1 answer:
lilavasa [31]2 years ago
7 0

Answer:

P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients
  • Expand by FOIL (First Outside Inside Last)
  • Factoring

<u>Geometry</u>

Perimeter Formula [Triangle]: P = L₁ + L₂ + L₃

  • L₁ is one side
  • L₂ is another side
  • L₃ is the 3rd side

Step-by-step explanation:

<u>Step 1: Define</u>

L₁ = (6a - 3b)(6a - 3b)

L₂ = (5a + 5c)(5a + 5c)

L₃ = (8c - b)(8c - b)

<u>Step 2: Find Perimeter</u>

  1. Substitute in variables [Perimeter - Triangle]:                                              P = (6a - 3b)² + (5a + 5c)² + (8c - b)²
  2. Expand [FOIL]:                                                                                                P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)
  3. Combine like terms (a²):                                                                                 P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²
  4. Combine like terms (b²):                                                                                P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²
  5. Combine like terms (c²):                                                                                P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bc
  6. Rearrange variables:                                                                                      P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bc
  7. Factor:                                                                                                             P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc
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