Question

The vertices of a triangle are (2,2), (-4,-1) and (1.4) what is the perimeter ?

Answer 1

`\sf 4√(5)+5√(2) \ units`

Explanation:

Perimeter of triangle when co-ordinates of the vertices are given:

First find the length of each side using distance formula. Then find the perimeter by adding all the sides.

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

A(2 , 2) ⇒ x₁= 2 & y₁ = 2

B(-4, -1) ⇒ x₂ = -4 & y₂ = -1

`\sf AB = √((-4-2)^2+(-1-2)^2)\\\\ ~ ~ ~ \ = √((-6)^2+(-3)^2) \\\\~~~ \ = √(36+9)\\\\~~~ \ = √(45)\\\\`

`\sf = √(3*3*5)\\\\=3√(5) \ units`

B(-4, -1) ⇒ x₁ = -4 & y₁ = -1

C(1, 4) ⇒ x₂ = 1 & y₂ = 4

`\sf BC = √((1-[-4])^2+(4-[-1])^2)`

`\sf = √((1+4)^2+(4+1)^2)\\\\=√((5)^2+(5)^2)\\\\=√(25+25)\\\\=√(50)\\\\=√(2*5*5)\\\\=5√(2)`

A(2 , 2) ⇒ x₁= 2 & y₁ = 2

C(1, 4) ⇒ x₂ = 1 & y₂ = 4

`AC= √((1-2)^2+(4-2)^2)\\`

`\sf =√((-1)^2+(2)^2)\\\\=√(1+4)\\\\=√(5) \ units`

`\sf Perimeter = 3√(5)+5√(2)+√(5)`

`\sf = √(5) (3+1) + 5√(2)\\\\=4√(5)+5√(2)`