Math Problem Statement
triangle CDE ~ triangle pqr. CD = 9m, EC = 15m, PQ = 15m. What is the length of RP.
Solution
Since triangle is similar to triangle , we can use the property of similar triangles. In similar triangles, the corresponding sides are proportional. That is:
Now, let's plug in the known values:
To solve for , cross-multiply:
Now, divide both sides by 9:
So, the length of is 25 meters.
Would you like further details or clarification on any part of the solution?
Here are some related questions to explore:
- What other properties do similar triangles have?
- How can you prove that two triangles are similar?
- What is the difference between similar and congruent triangles?
- How would the solution change if the triangles weren't similar?
- Can we apply this proportionality method in non-triangular figures?
Tip: When working with similar triangles, always make sure to match the corresponding sides carefully for accurate results.
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Math Problem Analysis
Mathematical Concepts
Similar Triangles
Proportionality
Formulas
\frac{CD}{PQ} = \frac{EC}{RP}
Theorems
Properties of Similar Triangles
Suitable Grade Level
Grades 7-9