Math Problem Statement
Solution
In this problem, we have two similar triangles, and . The side lengths of these triangles are given, and we are asked to find the length of (denoted as in the diagram).
Step-by-Step Solution
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Identify the corresponding sides: Since the triangles are similar, their corresponding sides are proportional. This gives us:
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Assign known values to the ratios:
- (unknown)
Using the proportion:
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Solve for : Cross-multiply to solve for :
Answer
The length of is approximately 78.5.
Would you like more details on the solution or have any questions?
Here are some related questions for further understanding:
- How do you identify corresponding sides in similar triangles?
- What is the cross-multiplication method, and how does it work in proportions?
- Why are similar triangles useful in solving for unknown lengths?
- How do you round numbers to the nearest tenth, and why is it necessary here?
- What other real-life applications use triangle similarity and proportional reasoning?
Tip: Always double-check which sides correspond in similar triangles, as this ensures accurate setting up of the proportion.
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Math Problem Analysis
Mathematical Concepts
Geometry
Similarity of Triangles
Proportions
Formulas
\( \frac{FG}{IJ} = \frac{GH}{JK} \)
Theorems
Similarity Theorem for Triangles
Suitable Grade Level
Grades 8-10