What is the perimeter of a triangle with corners at #(6 ,4 )#, #(8 ,2 )#, and #(5 ,7 )#?

Using Distance Formula

Find distance between (6,4),(8,2) and (8,2),(5,7) and (5,7),(6,4)

Add them we get Perimeter of the Triangle

Reference

To find the perimeter of a triangle with coordinates of its vertices given, you need to calculate the distance between each pair of adjacent vertices and then sum up these distances.

Using the distance formula: [ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

For the first two points (6, 4) and (8, 2): [ \text{Distance} = \sqrt{(8 - 6)^2 + (2 - 4)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} ]

For the second two points (8, 2) and (5, 7): [ \text{Distance} = \sqrt{(5 - 8)^2 + (7 - 2)^2} = \sqrt{(-3)^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} ]

For the last two points (5, 7) and (6, 4): [ \text{Distance} = \sqrt{(6 - 5)^2 + (4 - 7)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} ]

Now, summing up the distances: [ \text{Perimeter} = \sqrt{8} + \sqrt{34} + \sqrt{10} ]

Thus, the perimeter of the triangle is the sum of these distances, which is approximately equal to ( \sqrt{8} + \sqrt{34} + \sqrt{10} ).