# Given the points A(2,0), B(4,2), C(3,4), calculate the perimeter of ABC triangle.

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We have the triangle ABC :

A(2,0) B(4,2) C(3,4)

Let us calculate the measure of the sides:

AB = sqrt[(4-2)^2 + (2-0)^2]= sqrt2+4 = sqrt8 = 2sqrt2

BC = sqrt[(3-4)^2 + (4-2)^2]= sqrt(1+4)= sqrt5

AC= sqrt[(3-2)^2 + (4-0)^2]= sqrt(1+16) = sqrt17

Then the perimeter is:

P= AB + AC + BC

= 2sqrt2 + sqrt5 + sqrt17

Perimeter of the triangle ABC is equal to the sum of the lengths of the three sides. Thus:

Perimeter = AB + BC + CA

Length of any line joining two points (x1, y1) and (x2, y2) is given by the formula:

Length of line = [(x2 - x1)^2 + (y2 - y1)^2]^(1/2)

Using the above formula we calculate the length of three side of the triangle ABC as follows:

AB = [(4 - 2)^2 + (2 - 0)^2]^(1/2

= (2^2 + 2^2)^(1/2)

= (4 + 4)^1/2

= 8^(1/2)

BC = [(3 - 4)^2 + (4 - 2)^2]^(1/2)

= [(-1)^2 + 2^2]^(1/2)

= (1 + 4)^(1/2)

= 5^(1/2)

CA = [(2 - 3)^2 + (0 - 4)^2]^(1/2)

= [(-1)^2 + (-4)^2]^(1/2)

= (1 + 16)^(1/2)

= 17^1/2

Substituting value of AB, BC and CA in formula for perimeter:

Perimeter of ABC = 8^(1/2) + 5^(1/2) + 17^(1/2)

= 9.1876

To calculate perimeter Of triangle ABC.

A(2,0),B(4,2), C(3,4)

Solution:

The distance d between the points P1(x1,y1) and P2(x2,y2) is given by:

d = P1P2= sqrt{ (x2-x1)^2+(y2-y1)^2}.

Therefore,

AB = sqrt{(4-2)^2+(2-0)^2} = sqrt(4+4} = sqert8 = 2srt2.

BC = sqrt{(3-4)^3+(4-2)^2} = sqrt{1+4 } = sqrt5

CA = sqrt{(2-3)^2+(0-4)^2} = sqrt(1+16} = sqrt17.

Therfore the perimeter of ABC = AB+BC+CA = (2sqrt2+sqrt5+sqrt17} = 9.1876 units.

To determine the value of the perimeter of the triangle ABC,we'll calculate the sum of the length of the sides of ABC.

P = AB+AC+BC

We'll calculate the length of AB:

AB = sqrt [(xB-xA)^2 + (yB-yA)^2]

AB = sqrt[(4-2)^2 + (2-0)^2]

AB = sqrt 8

AB = 2*sqrt 2

We'll calculate the length of AC:

AC = sqrt [(xC-xA)^2 + (yC-yA)^2]

AC = sqrt [(3-2)^2 + (4-0)^2]

AC = sqrt 17

BC = sqrt [(xC-xB)^2 + (yC-yB)^2]

BC = sqrt [(3-4)^2 + (4-2)^2]

BC = sqrt 5

**P = 2*sqrt 2 + sqrt 17 + sqrt 5**