Answer:
The length of the three sides [tex]5, \sqrt{58} , \sqrt{65}[/tex]
The triangle is not a right triangle
Step-by-step explanation:
A = (3, 2) , B = ( 6, 9) , C = (10, 6)
Find the lengths using distance formula.
[tex]distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}[/tex]
[tex]BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
[tex]AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}[/tex]
Using Pythagoras theorem :
[tex](Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides[/tex]
Longest side is AC . So we will check if it satisfies Pythagoras theorem :
[tex]\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25\\[/tex]
65 ≠ 58 + 25
So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.
