Question

Please answer this question with a decent explanation - thank you.

Answer 1

Answer: P≈15.5 units.

Explanation:

The perimeter of a triangle is equal to the sum of all its sides:

P = a + b + c,

where P is the perimeter and a, b, c are the sides of the triangle.

The segment length formula makes it possible to calculate the distance between two arbitrary points in the plane, provided that the coordinates of these points are known:

`\boxed {d=√((x_1-x_2)^2+(y_1-y_2)^2) }`

1) (1,6) (3,1) ⇒ x₁=1 x₂=3 y₁=6 y₂=1

`a=√((1-3)^2+(6-1)^2) \\\\a=√((-2)^2+5^2) \\\\a=√(4+25) \\\\a=√(29) \approx5.4\ units\\`

2) (1,6) (6,1) ⇒ x₁=1 x₂=6 y₁=6 y₂=1

`b=√((1-6)^2+(6-1)^2) \\\\b=√((-5)^2+5^2) \\\\b=√(25+25) \\\\b=√(50) \approx7.1\ units\\`

3) (3,1) (6,1) ⇒ x₁=3 x₂=6 y₁=1 y₂=1

`c=√((3-6)^2+(1-1)^2) \\\\c=√((-3)^2+0^2) \\\\a=√(9+0) \\\\a=√(9) =3\ units\\`

4) P=a+b+c

P≈5.4+7.1+3

P≈15.5 units.