Math Problem Statement
In the following figure , ST II QR , point S divides PQ in the ratio 4:5. If PT=1.6 cm , what is the length of PR ?
Solution
To solve this problem, we are given the following information:
- Point divides in the ratio 4:5.
- The length .
- We are asked to find the length of .
Step-by-Step Solution:
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Since , by using the Basic Proportionality Theorem (also known as Thales' theorem), the line segment divides in the same ratio that it divides .
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Let the total length of be denoted by .
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Point divides in the ratio 4:5, meaning that:
- The length of .
- The length of .
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We are also given that , and since , the entire segment corresponds to in the same ratio. This means:
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Using the ratio , we can set up the proportion:
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Solving for :
Thus, the length of is 3.6 cm.
Would you like further details or have any questions?
Here are 5 related questions to consider:
- How does the Basic Proportionality Theorem apply in various types of triangles?
- Can the theorem be used in 3D geometry, and if so, how?
- How does the division ratio change if and are not parallel?
- What would happen if the ratio of division was reversed (5:4)?
- How would the result change if you were asked for instead of ?
Tip: When working with ratios, always set up proportions carefully to ensure consistency between the terms being compared.
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Math Problem Analysis
Mathematical Concepts
Proportions
Ratios
Geometry
Formulas
Ratio formula: PS/PQ = PT/PR
Proportion formula: PT/PR = 4/9
Theorems
Basic Proportionality Theorem (Thales' Theorem)
Suitable Grade Level
Grades 8-10
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