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

Answer:

$\displaystyle P_{\triangle ABC} \approx 22.7$

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: $\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

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

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:                                                                                     $\displaystyle P_{\triangle ABC} = 7 + \sqrt{58} + \sqrt{65}$
4. Simplify:                                                                                                        $\displaystyle P_{\triangle ABC} \approx 22.7$