Question

Please help me it is due soon, please no links

Answer 1

Answer:

The length of the three sides $5, \sqrt{58} , \sqrt{65}$

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.

$distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}$

$AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}$

$BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$

$AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}$

Using Pythagoras theorem :

$(Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides$

Longest side is AC . So we will check if it satisfies Pythagoras theorem :

$\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25$

65 ≠ 58 + 25

So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.