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

Let a, b, c be the sides. Sum of the three sides will give the perimeter.

To find the perimeter of the triangle, we need to calculate the distance between each pair of points and then sum these distances. Using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, we can compute the distances between the given points:

1. Between (1, 4) and (6, 3): $d_1 = \sqrt{(6 - 1)^2 + (3 - 4)^2} = \sqrt{5^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26}$

2. Between (1, 4) and (4, 2): $d_2 = \sqrt{(4 - 1)^2 + (2 - 4)^2} = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13}$

3. Between (6, 3) and (4, 2): $d_3 = \sqrt{(4 - 6)^2 + (2 - 3)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5}$

Now, we sum these distances to find the perimeter:

Perimeter = $d_1 + d_2 + d_3 = \sqrt{26} + \sqrt{13} + \sqrt{5}$