Math Problem Statement
Use the Segment Addition Postulate to find the length of ST. Given RS = 2x + 14, ST = 3x - 6, and RT = 53.
Solution
The problem asks us to use the Segment Addition Postulate to find the length of .
Given:
Using the Segment Addition Postulate, we know: Substitute the given expressions: Now solve for :
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Combine like terms:
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Subtract 8 from both sides:
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Divide by 5:
Now that we know , we can substitute it back into the expression for to find its length:
Thus, the length of is 21 units.
Let me know if you want any details or explanations on any step!
Here are 5 related questions for further practice:
- If and , and , what is the value of ?
- Can you derive the equation for from the diagram alone?
- How would the solution change if instead of ?
- What does the Segment Addition Postulate imply about points on a straight line?
- Can you verify the result by checking all segment lengths?
Tip: Always substitute the found values back into the original expressions to ensure the calculations are consistent!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Segment Addition Postulate
Formulas
RS + ST = RT
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 8-10