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

See a solution process below:

The perimeter of a triangle is:

We need to find the distance between each of the points in the problem. The formula for calculating the distance between two points is:

Distance Between (2, 6) and (4, 5) is:

Distance Between (2, 6) and (3, 1) is:

Distance Between (4, 5) and (3, 1) is:

The Perimeter of the Triangle is:

If you need a single number answer:

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To find the perimeter of the triangle with corners at (2, 6), (4, 5), and (3, 1), we need to find the lengths of each side and then sum them up.

Using the distance formula, the lengths of the sides are:

Side 1: between (2, 6) and (4, 5) [ \sqrt{(4-2)^2 + (5-6)^2} = \sqrt{2^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} ]

Side 2: between (2, 6) and (3, 1) [ \sqrt{(3-2)^2 + (1-6)^2} = \sqrt{1^2 + (-5)^2} = \sqrt{1 + 25} = \sqrt{26} ]

Side 3: between (4, 5) and (3, 1) [ \sqrt{(3-4)^2 + (1-5)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} ]

Now, sum up the lengths of the sides to find the perimeter:

[ \text{Perimeter} = \sqrt{5} + \sqrt{26} + \sqrt{17} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Circle A has a center at #(2 ,7 )# and a radius of #3 #. Circle B has a center at #(7 ,2 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?
- A triangle has corners at #(1 ,6 )#, #(7 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(1 ,3 )# and an area of #45 pi#. Circle B has a center at #(2 ,7 )# and an area of #75 pi#. Do the circles overlap?
- What is the perimeter of a triangle with corners at #(3 ,7 )#, #(2 ,3 )#, and #(4 ,9 )#?
- A line passes through #(5 ,8 )# and #(2 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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