Mathematics, 17.04.2020 23:10 laceysmith2i023

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

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Answer from: ponyolovezsosuk1074

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Coordinate Planes

Coordinates (x, y)

Geometry

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

s₁ is one sides₂ is 2nd sides₃ 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.

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

Step 3: Find Perimeter

Define sides: $\displaystyle s_1 = \overline{AB} ,\ s_2 = \overline{BC} ,\ s_3 = \overline{AC}$ Substitute in variables [Perimeter of a Triangle Formula]: $\displaystyle P_{\triangle ABC} = \overline{AB} + \overline{BC} + \overline{AC}$ Substitute in values: $\displaystyle P_{\triangle ABC} = 7 + \sqrt{58} + \sqrt{65}$ Simplify: $\displaystyle P_{\triangle ABC} \approx 22.7$

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

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