Math Problem Statement
CDE is an isosceles triangle with D E . If CD = 4x + 9, DE = 7x – 5, and CE = 16x – 27, find x and the measure of each side.
Solution
In an isosceles triangle, two sides are equal in length. Since is isosceles with , we know that sides and are equal.
Thus, we set up the equation: Substitute the given expressions for and :
Step 1: Solve for
- Rearrange the equation to isolate :
- Divide by 12:
Step 2: Find the Measure of Each Side
Now that we know , substitute it into each expression for , , and to find their lengths.
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For :
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For :
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For :
Solution Summary
The measures of the sides are:
Would you like more details on any step or have further questions?
Here are five related questions to deepen your understanding:
- What properties define an isosceles triangle, and why do they apply here?
- How would the solution change if it were specified that instead?
- What are the implications of equal angles in an isosceles triangle?
- Can you find the perimeter of with the values found?
- How does solving for help determine all unknowns in such geometry problems?
Tip: Always check your final values by substituting them back into original equations to verify consistency.
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Math Problem Analysis
Mathematical Concepts
Algebra
Isosceles Triangles
Equations
Formulas
Equation for equal sides in isosceles triangle
Linear equation solution
Theorems
Isosceles triangle properties
Suitable Grade Level
Grades 7-9
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