Final answer:
The measures of the sides of triangle RST with vertices R(0,2), S(2,5), and T(4,2) are found using the distance formula. After calculations, RS and ST both measure √13, and RT measures 4. Therefore, triangle RST is classified as an isosceles triangle.
Step-by-step explanation:
To find the measures of the sides of triangle RST with vertices R(0,2), S(2,5), and T(4,2), we need to apply the distance formula between each pair of points. The distance formula is √((x2-x1)² + (y2-y1)²), which comes from the Pythagorean theorem for calculating the hypotenuse of a right-angled triangle.
The lengths of the sides are calculated as follows:
- RS = √((2-0)² + (5-2)²) = √(4 + 9) = √13
- ST = √((4-2)² + (2-5)²) = √(4 + 9) = √13
- RT = √((4-0)² + (2-2)²) = √(16) = 4
After finding the side lengths, we can classify the triangle by its sides. Since RS and ST are of equal length and RT is different, triangle RST is an isosceles triangle.