Question

If the length of AC is2x and the length of BC is 3x-5, the value of x is

Answer 1

Answer:

The value of x is 5 units.

Step-by-step 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.

Hope this Helps!!!