Final answer:
The value of x cannot be determined based on the given information. The lengths of RS, ST, and RT cannot be calculated without a specific value for x. The perimeter of the triangle cannot be determined without knowing the exact lengths of the sides.
Step-by-step explanation:
In the given triangle ABC, we are given that RS = 2s + 10, ST = 3x - 2, and RT = 3x + 28. We are also told that triangle ARST is equiangular, which means that all three angles of the triangle are equal.
To find the value of x, we can set the two expressions for ST and RT equal to each other and solve for x. 3x - 2 = 3x + 28. Subtracting 3x from both sides gives -2 = 28, which is not true. Therefore, there is no single value for x that satisfies this equation.
Similarly, to find the lengths of RS, ST, and RT, we can substitute the given expressions into their corresponding variables. RS = 2s + 10, ST = 3x - 2, RT = 3x + 28. However, without a specific value for x, we cannot calculate the exact lengths of RS, ST, and RT.
Finally, to find the perimeter of the triangle, we can add up the lengths of all three sides. However, since we do not have specific values for RS, ST, and RT, we cannot calculate the exact perimeter of the triangle.