Question

A triangle has vertices (4,-2), (-3,0), and (1, 3). What is the approximate perimeter of the triangle?

a) 16
b) 17
c) 18
d) 15

Answer 1

The approximate perimeter of the triangle with vertices at (4,-2), (-3,0), and (1, 3) is found by calculating the lengths of the sides using the distance formula and summing those lengths. After computations, the perimeter is approximately 18 units.

Step-by-step explanation:

To find the approximate perimeter of the triangle with vertices at (4,-2), (-3,0), and (1, 3), we first need to calculate the lengths of the triangle's sides using the distance formula which is √((x2-x1)² + (y2-y1)²).

The distances between the vertices are:

• Distance between (4, -2) and (-3, 0) ≈ √((4 + 3)² + (-2 - 0)²) = √(49 + 4) ≈ 7.28.
• Distance between (-3, 0) and (1, 3) ≈ √((-3 - 1)² + (0 - 3)²) = √(16 + 9) ≈ 5.
• Distance between (1, 3) and (4, -2) ≈ √((1 - 4)² + (3 + 2)²) = √(9 + 25) ≈ 5.83.

Now, we add these distances together to get the perimeter: 7.28 + 5 + 5.83 ≈ 18.11, which is approximately 18 units. So, the correct answer is c) 18.