Answer:
Because the side of the triangle forms pythagoras tripple
Line AB = √10
Line BC = 10
Line AC = √90
Explanation:
From the question,
In the triangle,
Line AB = √[(8-5)²+(5-6)²]
Line AB = √(3²+-1²)
Line AB = √(9+1)
Line AB = √10
Also,
Line BC = √[(2-8)²+(-3-5)²]
Line BC = √(-6²+(-8)²)
Line BC = √(36+64)
Line BC = √100
Line BC = 10 unit.
Finally,
Line AC = √[(5-2)²+(6+3)²]
Line AC = √(3²+9²)
Line AC = √(9+81)
Line AC = √90.
From the above length of the line in the triangle,
Line AC, Line BC and Line AC are pythagoras triple.
I.e
10² = (√10)²+(√90)²
100 = 10+90
100 = 100.
Note only a a right angle triangle obeys pythagoras theorem.