What is the perimeter of a triangle with corners at #(7 ,9 )#, #(8, 2 )#, and #(9 ,4 )#?
Perimeter
compute lengths of sides:
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The perimeter of the triangle can be calculated by finding the sum of the lengths of its three sides using the distance formula.
Let's denote the vertices of the triangle as follows:
A(7, 9), B(8, 2), and C(9, 4).
Using the distance formula ( \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ), we can find the lengths of each side of the triangle: AB, BC, and AC.

Length of side AB: ( \sqrt{(8  7)^2 + (2  9)^2} = \sqrt{(1)^2 + (7)^2} = \sqrt{1 + 49} = \sqrt{50} )

Length of side BC: ( \sqrt{(9  8)^2 + (4  2)^2} = \sqrt{(1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5} )

Length of side AC: ( \sqrt{(9  7)^2 + (4  9)^2} = \sqrt{(2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29} )
Finally, the perimeter of the triangle is the sum of these side lengths:
Perimeter ( = AB + BC + AC )
Perimeter ( = \sqrt{50} + \sqrt{5} + \sqrt{29} )
Therefore, the perimeter of the triangle is ( \sqrt{50} + \sqrt{5} + \sqrt{29} ) 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.
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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