A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsExpand by FOIL (First Outside Inside Last)Factoring

Geometry

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

L₁ is one sideL₂ is another sideL₃ is the 3rd side

Step-by-step explanation:

Step 1: Define

L₁ = (6a - 3b)(6a - 3b)

L₂ = (5a + 5c)(5a + 5c)

L₃ = (8c - b)(8c - b)

Step 2: Find Perimeter

Substitute in variables [Perimeter - Triangle]:                                              P = (6a - 3b)² + (5a + 5c)² + (8c - b)²Expand [FOIL]:                                                                                                P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)Combine like terms (a²):                                                                                 P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²Combine like terms (b²):                                                                                P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²Combine like terms (c²):                                                                                P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bcRearrange variables:                                                                                      P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bcFactor:                                                                                                             P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc