Math Problem Statement
In the figure, ZY ≅ XW, ZX = 5x + 17, YW = 10 - 2x, and YX = 3. Find ZY and XW.
Solution
Let's analyze the given information from the problem.
- , which means the lengths of segments and are equal.
We are asked to find the lengths of and , knowing that .
Step-by-step approach:
- Since , we know that . The length of can be expressed as the difference between and . So:
- Similarly, the length of can be expressed as the difference between and :
- Since , we can set the two equations equal to each other:
- Solve for :
- Now substitute back into the expressions for and to find their lengths:
Therefore, both and have lengths of 9 units.
Final Answer:
Would you like a further explanation or details on any step?
Here are five related questions to deepen your understanding:
- How would the problem change if was a quadratic function of ?
- Can you find the value of using the value of ?
- What would happen if and were not congruent?
- How does the equality of segment lengths help solve this problem?
- How would you graph the relationships between these segments on a coordinate plane?
Tip: Always double-check if geometric figures suggest congruence or equality in length; it can simplify solving equations in geometry problems.
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Math Problem Analysis
Mathematical Concepts
Geometry
Congruence
Algebraic Equations
Formulas
ZY = ZX - YX
XW = YW - YX
ZY = XW
Theorems
Congruent Segments Theorem
Suitable Grade Level
Grades 9-10