Answer:
The value of x is 5 units.
Explanation:
Complete Question
In the figure CD is the perpendicular bisector of AB. If the length of AC is 2x and the length of BC is 3x - 5 . The value of x is ?
The figure is presented in the attached image to this solution.
Solution
Using the concept of similar triangles,
We can prove that triangles CDA is similar to triangle CDB.
This can be proved using the SAS congruence property that two sides and an angle between them are the same.
- Side AD = Side DB (Given in the diagram)
- Angle CDA = Angle CDB = 90° (Also evident from the diagram)
- Side CD = Side CD (common side to the two triangles)
Hence, it is evident that
Side AC = Side CB
2x = 3x - 5
3x - 2x = 5
x = 5 units.
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