Math Problem Statement

triangle CDE ~ triangle pqr. CD = 9m, EC = 15m, PQ = 15m. What is the length of RP.

Solution

Since triangle CDECDE is similar to triangle PQRPQR, we can use the property of similar triangles. In similar triangles, the corresponding sides are proportional. That is:

CDPQ=ECRP\frac{CD}{PQ} = \frac{EC}{RP}

Now, let's plug in the known values:

915=15RP\frac{9}{15} = \frac{15}{RP}

To solve for RPRP, cross-multiply:

9×RP=15×159 \times RP = 15 \times 15

9×RP=2259 \times RP = 225

Now, divide both sides by 9:

RP=2259=25mRP = \frac{225}{9} = 25 \, \text{m}

So, the length of RPRP is 25 meters.

Would you like further details or clarification on any part of the solution?

Here are some related questions to explore:

  1. What other properties do similar triangles have?
  2. How can you prove that two triangles are similar?
  3. What is the difference between similar and congruent triangles?
  4. How would the solution change if the triangles weren't similar?
  5. 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