Question

Find the perimeter of the triangle to the nearest whole unit.
18.
16.
14.
12.

Answer 1

Answer:

14

Step-by-step explanation:

Perimeter of the ∆ = sum of the length of the 3 sides.

The length of the 3 sides can be calculated by using the distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, to find the distance between the vertices of the ∆.

The coordinates of the 3 vertices are:

(-1, 3), (2, 2), (-2, -2)

Distance between (-1, 3) and (2, 2):

Let,

$(-1, 3) = (x_1, y_1)$

$(2, 2) = (x_2, y_2)$

$d = \sqrt{(2 -(-1))^2 + (2 - 3)^2}$

$d = \sqrt{(3)^2 + (-1)^2}$

$d = \sqrt{9 + 1} = \sqrt{10} = 3.2 units$

Distance between (2, 2) and (-2, -2)

Let,

$(2, 2) = (x_1, y_1)$

$(-2, -2) = (x_2, y_2)$

$d = \sqrt{(-2 - 2)^2 + (-2 - 2)^2}$

$d = \sqrt{(-4)^2 + (-4)^2}$

$d = \sqrt{16 + 16} = \sqrt{32} = 5.7 units$

Distance between (-2, -2) and (-1, 3)

Let,

$(-2, -2) = (x_1, y_1)$

$(-1, 3) = (x_2, y_2)$

$d = \sqrt{(-1 -(-2))^2 + (3 -(-2))^2}$

$d = \sqrt{(1)^2 + (5)^2}$

$d = \sqrt{1 + 25} = \sqrt{26} = 5.1 units$

Perimeter of triangle = 3.2 + 5.7 + 5.1 = 14.0 units