Final answer:
To find the length of ST, we need to apply the properties of a perpendicular bisector. Given that UT = 8y - 12 and ST = 3y, we can equate UT to ST and solve for y. Substituting y back into ST, we find that the length of ST is 7.2.
Step-by-step explanation:
To find the length of ST, we need to apply the properties of a perpendicular bisector. The perpendicular bisector of a line segment divides it into two congruent parts. In this case, RT is the perpendicular bisector of US. Since UT and ST are two congruent parts of US, they have the same length.
Given that UT = 8y - 12, we can equate it to ST:
8y - 12 = 3y
Now, we can solve for y:
8y - 3y = 12
5y = 12
y = 12/5
Substituting y back into ST:
ST = 3(12/5) = 36/5 = 7.2
Therefore, the length of ST is 7.2.