Question

Find the perimeter of triangle ABC. Round to the nearest tenth if necessary. A(-3,4),B(4,4)C(1,-3)

Answer 1

`\displaystyle P_(\triangle ABC) \approx 22.7`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

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

• Left to Right

Algebra I

Coordinate Planes

• Coordinates (x, y)

Geometry

Perimeter of a Triangle Formula: P = s₁ + s₂ + s₃

• s₁ is one side
• s₂ is 2nd side
• s₃ is 3rd side

Algebra II

Distance Formula:
`\displaystyle d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Explanation:

Step 1: Define

Identify.

Vertice A(-3, 4)

Vertice B(4, 4)

Vertice C(1, -3)

Step 2: Find Side Lengths

Simply plug in the 2 coordinates into the distance formula to find distance d.

1. [Side AB] Substitute in points [Distance Formula]:
   `\displaystyle \overline{AB} = √((4 - -3)^2 + (4 - 4)^2)`
2. [Side AB] Evaluate [Order of Operations]:
   `\displaystyle \overline{AB} = 7`
3. [Side BC] Substitute in points [Distance Formula]:
   `\displaystyle \overline{BC} = √((1 - 4)^2 + (-3 - 4)^2)`
4. [Side BC] Evaluate [Order of Operations]:
   `\displaystyle \overline{BC} = √(58)`
5. [Side AC] Substitute in points [Distance Formula]:
   `\displaystyle \overline{AC} = √((1 - -3)^2 + (-3 - 4)^2)`
6. [Side AC] Evaluate [Order of Operations]:
   `\displaystyle \overline{AC} = √(65)`

Step 3: Find Perimeter

1. Define sides:
   `\displaystyle s_1 = \overline{AB} ,\ s_2 = \overline{BC} ,\ s_3 = \overline{AC}`
2. Substitute in variables [Perimeter of a Triangle Formula]:
   `\displaystyle P_(\triangle ABC) = \overline{AB} + \overline{BC} + \overline{AC}`
3. Substitute in values:
   `\displaystyle P_(\triangle ABC) = 7 + √(58) + √(65)`
4. Simplify:
   `\displaystyle P_(\triangle ABC) \approx 22.7`