# What is the perimeter of a triangle with corners at #(1 ,5 )#, #(6 ,3 )#, and #(4 ,2 )#?

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To find the perimeter of the triangle, calculate the distance between each pair of points and sum them up.

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

(d_1 = \sqrt{(6 - 1)^2 + (3 - 5)^2} = \sqrt{5^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29})

(d_2 = \sqrt{(4 - 6)^2 + (2 - 3)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5})

(d_3 = \sqrt{(4 - 1)^2 + (2 - 5)^2} = \sqrt{3^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18})

Adding the distances:

(Perimeter = d_1 + d_2 + d_3 = \sqrt{29} + \sqrt{5} + \sqrt{18})

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