Math Problem Statement
Solution
This problem involves using the geometric mean theorem for a right triangle with an altitude drawn to the hypotenuse. Here’s how to solve it step by step:
Key Information:
- Altitude forms two similar right triangles.
According to the geometric mean theorem:
Step-by-Step Solution:
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Substitute the values of and into the formula:
-
Simplify the product:
-
Simplify to its simplest radical form:
Final Answer:
Would you like further clarification or details about the steps?
Relative Questions:
- How does the geometric mean theorem apply to right triangles?
- What are other properties of similar triangles in this setup?
- How can you simplify square roots systematically?
- What are the conditions for triangles to be similar?
- How is the hypotenuse related to the legs and altitude in a right triangle?
Tip:
Always verify whether the given lengths satisfy the properties of right triangles (e.g., as the hypotenuse equals ).
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Math Problem Analysis
Mathematical Concepts
Right triangles
Geometric mean
Simplifying square roots
Formulas
BD = √(AD × DC)
Theorems
Geometric mean theorem
Suitable Grade Level
Grades 8-10
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