Answer: The lengths of the sides of the given triangle are 5 units, 5 units, √2 units. The triangle is isosceles.
Step-by-step explanation: The given co-ordinates of the vertices of a triangle are A(3, 5), B(6, 9), C(2, 6).
We are find the lengths of the sides of the triangle and to identify the type of the triangle.
The lengths of the three sides AB, BC and CA of the given triangle are calculated using distance formula as follows :
[tex]AB=\sqrt{(6-3)^2+(9-5)^2}=\sqrt {9+16}=\sqrt{25}=5~\textup{units},\\\\BC=\sqrt{(2-6)^2+(6-9)^2}=\sqrt {16+9}=\sqrt{25}=5~\textup{units},\\\\CA=\sqrt{(3-2)^2+(5-6)^2}=\sqrt {1+1}=\sqrt2~\textup{units}[/tex]
Since the lengths of the two sides AB and BC are equal, so teh given triangle is isosceles.
Thus, the given triangle is isosceles.
