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valentina_108 [34]
2 years ago
11

Given below are the coordinates of the vertices of a triangle. Find the lengths of the sides of the triangle, then click to iden

tify the triangle as scalene, isosceles, or equilateral.
R(1, 3), S(3, 1), T(5, 2)

Mathematics
1 answer:
Shkiper50 [21]2 years ago
4 0
To find the length of the sides, we use the Pythagorean Theorem. First, let's look at the side RS. R is at (1,3), and S is at (3,1). Therefore, to find RS, we use the difference in height and length:a =  \sqrt{ {b}^{2}  +  {c}^{2} }  \\ a =  \sqrt{ {(3 - 1)}^{2} +  {(1 - 3)}^{2}  }  \\ a =  \sqrt{ {(2)}^{2} +  {( - 2)}^{2}  } \\  a =  \sqrt{4 + 4} \\ a =  \sqrt{8}
The length of side RS is square root 8.

Side ST is made from point S (3,1) and point T (5,2).
a =  \sqrt{ {(5 - 3)}^{2} +  {(2 - 1)}^{2}  }  \\ a =  \sqrt{ {(2)}^{2} +  {(1)}^{2}  }  \\ a =  \sqrt{4 + 1}  \\ a =  \sqrt{5}
The length of side ST is root 5.

Side RT is between R (1,3) and T (5,2).
a =  \sqrt{ {(1 - 5)}^{2}  + {(3 - 2)}^{2} }  \\ a =  \sqrt{ {( - 4)}^{2} +  {(1)}^{2}  }  \\ a =  \sqrt{16 + 1}  \\ a =  \sqrt{17}
The side RT is root 17. The triangle is scalene, meaning it has three sides of different lengths.

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