What is the perimeter of a triangle with corners at #(1 ,4 )#, #(6 ,3 )#, and #(4 ,2 )#?
Perimeter = 10.995
Let a, b, c be the sides. Sum of the three sides will give the perimeter.
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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:

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})

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})

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})
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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 ,4 )# and an area of #81 pi#. Circle B has a center at #(4 ,3 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?
 An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(2 ,5 )# to #(8 ,1 )# and the triangle's area is #15 #, what are the possible coordinates of the triangle's third corner?
 What is the perimeter of a triangle with corners at #(1 ,5 )#, #(8 ,3 )#, and #(4 ,1 )#?
 Circle A has a center at #(2 ,8 )# and a radius of #2 #. Circle B has a center at #(8 ,3 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
 A triangle has corners at #(3 ,5 )#, #(4 ,7 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?
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