The Vertices Of The Triangle Are \[$(-6,-4)\$\], \[$(-6,5)\$\], And \[$(5,4)\$\]. What Is The Perimeter Of The Triangle? Round The Answer To The Nearest Tenth If Necessary.A. 33.6 Units B. 30.3 Units C. 27.2 Units D. 35.1 Units

**The Vertices of a Triangle: Calculating the Perimeter**

What is the Perimeter of a Triangle?

The perimeter of a triangle is the total distance around the triangle. It is calculated by adding up the lengths of all three sides of the triangle.

Calculating the Perimeter of a Triangle

To calculate the perimeter of a triangle, we need to find the lengths of all three sides. We can use the distance formula to find the lengths of the sides.

Distance Formula

The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between two points (x1, y1) and (x2, y2).

Finding the Lengths of the Sides

Let's use the distance formula to find the lengths of the sides of the triangle.

Side 1: (-6, -4) to (-6, 5) d1 = √((-6 - (-6))² + (5 - (-4))²) d1 = √(0² + 9²) d1 = √(81) d1 = 9

Side 2: (-6, 5) to (5, 4) d2 = √((5 - (-6))² + (4 - 5)²) d2 = √(11² + (-1)²) d2 = √(121 + 1) d2 = √(122) d2 = 11.0

Side 3: (5, 4) to (-6, -4) d3 = √((-6 - 5)² + (-4 - 4)²) d3 = √((-11)² + (-8)²) d3 = √(121 + 64) d3 = √(185) d3 = 13.6

Calculating the Perimeter

Now that we have the lengths of all three sides, we can calculate the perimeter.

Perimeter = d1 + d2 + d3 Perimeter = 9 + 11.0 + 13.6 Perimeter = 33.6

Rounding the Answer

We are asked to round the answer to the nearest tenth if necessary. Since 33.6 is already rounded to the nearest tenth, our final answer is:

The Final Answer is 33.6 units

Q&A

Q: What is the perimeter of a triangle? A: The perimeter of a triangle is the total distance around the triangle.

Q: How do I calculate the perimeter of a triangle? A: To calculate the perimeter of a triangle, you need to find the lengths of all three sides and add them up.

Q: What is the distance formula? A: The distance formula is d = √((x2 - x1)² + (y2 - y1)²), where d is the distance between two points (x1, y1) and (x2, y2).

Q: How do I find the lengths of the sides of a triangle? A: You can use the distance formula to find the lengths of the sides of a triangle.

Q: What is the perimeter of the triangle with vertices (-6, -4), (-6, 5), and (5, 4)? A: The perimeter of the triangle is 33.6 units.

Q: Do I need to round the answer to the nearest tenth? A: Yes, you need to round the answer to the nearest tenth if necessary.

Q: What is the final answer? A: The final answer is 33.6 units.