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:[tex]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} [/tex]
The length of side RS is square root 8.
Side ST is made from point S (3,1) and point T (5,2).
[tex]a = \sqrt{ {(5 - 3)}^{2} + {(2 - 1)}^{2} } \\ a = \sqrt{ {(2)}^{2} + {(1)}^{2} } \\ a = \sqrt{4 + 1} \\ a = \sqrt{5} [/tex]
The length of side ST is root 5.
Side RT is between R (1,3) and T (5,2).
[tex]a = \sqrt{ {(1 - 5)}^{2} + {(3 - 2)}^{2} } \\ a = \sqrt{ {( - 4)}^{2} + {(1)}^{2} } \\ a = \sqrt{16 + 1} \\ a = \sqrt{17} [/tex]
The side RT is root 17. The triangle is scalene, meaning it has three sides of different lengths.
