Math Problem Statement

What is the value of x in the geometric problem involving similar triangles with given dimensions?

Solution

This is a geometric problem involving similar triangles, where we use the proportionality of sides to solve for the unknown xx.

The two triangles are similar because they share an angle at CC, and both have right angles. The proportion between corresponding sides is:

9x=1535\frac{9}{x} = \frac{15}{35}

Cross-multiply to solve for xx:

935=15x9 \cdot 35 = 15 \cdot x

315=15x315 = 15x

x=31515=21x = \frac{315}{15} = 21

Thus, x=21x = 21.

Let me know if you need further clarification or additional details.

Expanding on the problem:

  1. What is the mathematical basis of triangle similarity in this problem?
  2. Can we use other methods, like trigonometry, to verify the result?
  3. How would the solution change if the lengths were different but the triangles remained similar?
  4. Can you calculate the area of each triangle given their side lengths?
  5. What are the properties of proportionality in triangles that apply here?

Tip: Always identify shared angles or side ratios in geometry problems to apply similarity rules effectively.

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Math Problem Analysis

Mathematical Concepts

Geometry
Similarity of Triangles
Proportions

Formulas

Proportionality of corresponding sides in similar triangles: (Side1 of Triangle A) / (Side2 of Triangle A) = (Side1 of Triangle B) / (Side2 of Triangle B)

Theorems

Triangle Similarity Theorem

Suitable Grade Level

Grades 8-10