What is the perimeter of a triangle with corners at #(7 ,2 )#, #(8 ,3 )#, and #(4 ,4 )#?
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To find the perimeter of a triangle with corners at (7, 2), (8, 3), and (4, 4), you need to calculate the lengths of the three sides of the triangle using the distance formula, and then sum them up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
[ d = \sqrt{(x2  x1)^2 + (y2  y1)^2} ]
Using this formula for each pair of points, we get:

Between (7, 2) and (8, 3): [ d_1 = \sqrt{(8  7)^2 + (3  2)^2} = \sqrt{1^2 + 1^2} = \sqrt{2} ]

Between (8, 3) and (4, 4): [ d_2 = \sqrt{(4  8)^2 + (4  3)^2} = \sqrt{(4)^2 + 1^2} = \sqrt{17} ]

Between (4, 4) and (7, 2): [ d_3 = \sqrt{(7  4)^2 + (2  4)^2} = \sqrt{3^2 + (2)^2} = \sqrt{13} ]
Now, summing up the lengths of the three sides:
[ Perimeter = d_1 + d_2 + d_3 = \sqrt{2} + \sqrt{17} + \sqrt{13} ]
So, the perimeter of the triangle is ( \sqrt{2} + \sqrt{17} + \sqrt{13} ) units.
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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.
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