Question

Find the exact length of each side. Then classify RTN by its sides.

Answer 1

first, we find the length of each side, then:

for TR

`\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(-8-(-6))^2+(-7-7)^2} \\ d=\sqrt[]{(-8+6)^2+(-14)^2} \\ d=\sqrt[]{(-2)^2+196} \\ d=\sqrt[]{4+196} \\ d=\sqrt[]{100}=10 \end{gathered}`

answer: TR = 10

for NT

`\begin{gathered} d=\sqrt[]{(-6-5)^2+(7-0)^2} \\ d=\sqrt[]{(-11)^2+7^2} \\ d=\sqrt[]{121+49} \\ d=\sqrt[]{170} \\ d=13.04 \end{gathered}`

answer: NT = 13.04

for RN

`\begin{gathered} d=\sqrt[]{(5-(-8))^2+(0-(-7))^2} \\ d=\sqrt[]{(5+8)^2+7^2} \\ d=\sqrt[]{13^2+49} \\ d=\sqrt[]{169+49} \\ d=\sqrt[]{218} \\ d=14.76 \end{gathered}`

answer: RN = 14.76

therefore the sides are:

10

13.04

14.76

so, If all three sides of the triangle are a different length then the triangle is a SCALENE triangle.

answer: RTN is scalene