Math Problem Statement
Find the value of x:
Solution
To find the value of in the given geometric configuration, we can use the properties of right triangles and the Pythagorean theorem.
Given:
- The right triangle with legs and
- The hypotenuse of this right triangle is 20
Using the Pythagorean theorem:
Here, , , and . Thus, we have:
Expanding and simplifying the equation:
Dividing the entire equation by 2 to simplify:
This is a quadratic equation of the form . We can solve it using the quadratic formula:
For our equation, , , and :
Since represents a length, we take the positive value:
Simplifying further:
Thus, the value of is:
Would you like further details or have any questions?
Here are five more questions you can ask:
- How do I solve another quadratic equation?
- Can you explain the steps of the quadratic formula?
- What are the properties of right triangles?
- How is the Pythagorean theorem used in different types of problems?
- How can I verify the solution to a geometric problem?
Tip: Always double-check your algebraic manipulations when solving equations to avoid small errors that can lead to incorrect solutions.
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Math Problem Analysis
Mathematical Concepts
Geometry
Pythagorean Theorem
Quadratic Equations
Formulas
Pythagorean theorem
Quadratic formula
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 9-12
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