An engineer is designing three triangular traffic signs with a computer program. The vertices of Sign A are located at (2, 2) , (2, 12) , and (17, 7) . The vertices of Sign B are located at (4,4),(11, 19) and (18, 4) . The vertices of Sign C are located at (4, 8), (24, 1) , and (24, 15) . Put the signs in order from largest to smallest perimeter. Sign A Sign B Sign C

sign C, sign B, sign A

Step-by-step explanation:

Given the vertices of triangular post A as (2, 2) , (2, 12) , and (17, 7). Let us find the length of side of the post using the formula for calculating distance between 2 points using the formula:

D = √(y₂-y₁)²+(x₂-x₁)²

For the coordinate (2, 2) , (2, 12)

S₁ = √(12-2)²+(2-2)²

S₁ = √(10)²+(0)²

S₁ = √100

S₁ = 10

For the coordinate (2, 2) , (17, 7)

S₂ = √(7-2)²+(17-2)²

S₂ = √(5)²+(15)²

S₂ = √25+225

S₂ = √250

S₂ = 15.8

For the coordinate (2, 12) , (17, 7)

S₃ = √(7-12)²+(17-2)²

S₃ = √(-5)²+(15)²

S₃ = √25+225

S₃ = √250

S₃ = 15.8

Perimeter of sign A = S₁+S₂+S₃

Perimeter of sign A = 10+15.8+15.8

Perimeter of sign A = 41.6

FOR SIGN B with coordinate of vertices (4,4),(11, 19) and (18, 4)

For the coordinate (4, 4) , (11, 19)

S₁ = √(19-4)²+(11-4)²

S₁ = √(15)²+(7)²

S₁ = √225+49

S₁ = 16.6

For the coordinate (4, 4) , (18, 4)

S₂ = √(4-4)²+(18-4)²

S₂ = √(0)²+(14)²

S₂ = √196

S₂ = 14

For the coordinate (11, 19) , (18, 4)

S₃ = √(4-19)²+(18-11)²

S₃ = √(-15)²+(7)²

S₃ = √225+49

S₃ = 16.6

Perimeter of sign B = S₁+S₂+S₃

Perimeter of sign B = 14+16.6+16.6

Perimeter of sign B = 47.2

FOR SIGN C with coordinate of vertices (4, 8), (24, 1) , and (24, 15)

For the coordinate (4, 8) , (24, 1)

S₁ = √(1-8)²+(24-4)²

S₁ = √(-7)²+(20)²

S₁ = √49+400

S₁ = 21.2

For the coordinate (4, 8) , (24, 15)

S₂ = √(15-8)²+(24-4)²

S₂ = √(7)²+(20)²

S₂ = √49+400

S₂ = 21.2

For the coordinate (24, 1) , (24, 15)

S₃ = √(15-1)²+(24-24)²

S₃ = √(14)²+(0)²

S₃ = √196+0

S₃ = 14

Perimeter of sign C = S₁+S₂+S₃

Perimeter of sign C = 14+21.2+21.2

Perimeter of sign C = 56.4

Arranging in order from largest to smallest perimeter, Sign C(56.4), Sign B (47.2), sign A (41.6)