Final answer:
To find the measures of the sides of triangle RST, use the distance formula on the coordinates of its vertices R, S, and T. RS and ST both measure approximately 3.61 units, and RT measures 4 units, classifying RST as an isosceles triangle.
Step-by-step explanation:
The question pertains to finding the measures of the sides of triangle RST given the coordinates of its vertices R(0,2), S(2,5), and T(4,2). By applying the distance formula √((x2-x1)² + (y2-y1)²) to calculate the length of each side, we can classify the triangle by its sides. Assuming there is a typographical error in the question with 'D' instead of 'S', we can proceed to find the lengths:
- RS = √((2-0)² + (5-2)²) = √(4+9) = √13 ≅ 3.61 units
- ST = √((4-2)² + (2-5)²) = √(4+9) = √13 ≅ 3.61 units
- RT = √((4-0)² + (2-2)²) = √(16+0) = 4 units
Since the lengths of RS and ST are approximately equal and RT is distinct, triangle RST is an isosceles triangle by its sides.
It is important to note that to use the Pythagorean theorem, a triangle must be a right triangle with one angle measuring 90 degrees, which does not necessarily apply here based on the given vertices. Instead, classifying by the sides after finding their measures is a suitable approach.