Math Problem Statement
Solution
The problem involves the Triangle Proportionality Theorem. According to this theorem, if a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally.
Here’s the given data:
- ,
- , (to be found).
Step-by-step solution:
-
Using the Triangle Proportionality Theorem, the ratios of the divided sides are equal:
-
Substitute the known values:
-
Simplify the first fraction:
-
Cross-multiply:
-
Solve for :
Thus, .
Would you like additional details or explanations?
Related Questions:
- What is the Triangle Proportionality Theorem and how does it work?
- How can we verify the ratios in triangle proportionality problems?
- What are some real-life applications of proportionality in geometry?
- What happens when the dividing line is not parallel to one side of the triangle?
- How does the Triangle Proportionality Theorem relate to similar triangles?
Tip:
When solving proportionality problems in triangles, always verify that the line dividing the two sides is parallel to the third side. This ensures the theorem is applicable.
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Math Problem Analysis
Mathematical Concepts
Geometry
Proportionality
Formulas
QR/RS = ST/TU
Theorems
Triangle Proportionality Theorem
Suitable Grade Level
Grades 8-10
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