Math Problem Statement
Find the missing side length in two similar triangles ΔABC and ΔPQR, given: AB = 5, AC = 6, PQ = 20, PR = 24, QR = 32, and BC = ?.
Solution
To solve for the missing side length in the two similar triangles and , we will use the property of similar triangles: corresponding sides are proportional.
Step 1: Identify the corresponding sides
From the given triangles:
- corresponds to ,
- corresponds to ,
- corresponds to .
The lengths are:
- , ,
- , ,
- , .
Step 2: Set up the proportion
Using the corresponding sides :
Step 3: Solve for
Simplify to :
Now, solve for by cross-multiplying:
Final Answer:
The missing side is 8.
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Related Questions:
- How do you prove two triangles are similar?
- What are the properties of similar triangles?
- How do you solve for an unknown side in similar triangles?
- How do you scale triangles using a ratio?
- Can the similarity ratio of triangles be used in real-life applications?
Tip:
Always ensure you set up proportions carefully when solving problems involving similar triangles!
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Math Problem Analysis
Mathematical Concepts
Similar Triangles
Proportionality
Cross-Multiplication
Formulas
Corresponding sides in similar triangles are proportional: AB/PQ = BC/QR
Theorems
Triangle Similarity Theorem
Proportionality Theorem
Suitable Grade Level
Grade 8-10