# What is the perimeter of a triangle with corners at #(3 ,0 )#, #(5 ,2 )#, and #(5 ,4 )#?

#2sqrt(2)+2sqrt(5)+2 ~~ 9.3#

These are the lengths of the three sides, so the perimeter is just the sum:

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To find the perimeter of a triangle with vertices at (3, 0), (5, 2), and (5, 4), you can use the distance formula between each pair of points and then sum up these distances.

The distance formula between two points ((x_1, y_1)) and ((x_2, y_2)) is given by:

[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

Using this formula for each pair of points, we get:

- Distance between (3, 0) and (5, 2):

[ \sqrt{(5 - 3)^2 + (2 - 0)^2} = \sqrt{2^2 + 2^2} = \sqrt{8} ]

- Distance between (3, 0) and (5, 4):

[ \sqrt{(5 - 3)^2 + (4 - 0)^2} = \sqrt{2^2 + 4^2} = \sqrt{20} ]

- Distance between (5, 2) and (5, 4):

[ \sqrt{(5 - 5)^2 + (4 - 2)^2} = \sqrt{0^2 + 2^2} = \sqrt{4} ]

Now, summing up these distances gives the perimeter:

[ \text{Perimeter} = \sqrt{8} + \sqrt{20} + \sqrt{4} = 2\sqrt{2} + 2\sqrt{5} + 2 ]

So, the perimeter of the triangle is ( 2\sqrt{2} + 2\sqrt{5} + 2 ) units.

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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.

- A triangle has corners at #(4 ,7 )#, #(2 ,6 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(5 ,-4 )# and a radius of #7 #. Circle B has a center at #(-6 ,-8 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
- A triangle has corners at #(4 ,3 )#, #(2 ,6 )#, and #(7 ,1 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(6 ,0 )#, #(5 ,2 )#, and #(5 ,4 )#?
- A line passes through #(2 ,5 )# and #(0 ,1 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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