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What is the perimeter of a triangle with corners at #(3 ,9 )#, #(5 ,7 )#, and #(1 ,4 )#?

Answer 1

Evelyn Arboleda

Perimeter of the triangle is # 13.22# unit

#A(3,9),B(5,7),C(1,4) # are the three vertices of triangle.

Distance between two points #(x_1,y_1) and (x_2,y_2)# is

#D= sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

#AB^2=(3-5)^2+(9-7)^2 =8 :. AB= sqrt 8~~2.83 # unit

#BC^2=(5-1)^2+(7-4)^2 =25 :. BC= 5 # unit

#CA^2=(1-3)^2+(4-9)^2 =29 :. CA= sqrt 29~~5.39 # unit

Perimeter of the triangle is #P=AB+BC+CA# or

#P=2.83+5.0+5.39 ~~13.22# unit [Ans]

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Answer 2

Claire Akin

The perimeter of the triangle can be calculated by finding the distance between each pair of points and then summing those distances. Using the distance formula ( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ) for each pair of points:

Distance between (3, 9) and (5, 7) is ( \sqrt{(5 - 3)^2 + (7 - 9)^2} = \sqrt{4 + 4} = \sqrt{8} ).
Distance between (5, 7) and (1, 4) is ( \sqrt{(1 - 5)^2 + (4 - 7)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 ).
Distance between (1, 4) and (3, 9) is ( \sqrt{(3 - 1)^2 + (9 - 4)^2} = \sqrt{4 + 25} = \sqrt{29} ).

Summing these distances gives the perimeter of the triangle: ( \sqrt{8} + 5 + \sqrt{29} ).

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Answer from HIX Tutor

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