Final answer:
To find the value of x, use the fact that the triangles are similar and set up a proportion equation.
Step-by-step explanation:
To find the value of x, we need to use the fact that the two triangles △ACB and △CDB are similar. This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional.
One pair of equations that will help us find the value of x is:
- (AC/CD) = (CB/BD)
- Using the given information, we can substitute the values AC = 34 and CB = x+8 into the equation:
- (34/CD) = (x+8/BD)
- By cross-multiplying, we can simplify the equation:
- 34BD = CD(x+8)
- Solving for x, we can rearrange the equation:
- x = (34BD/CD) - 8
These equations will help you find the value of x in the given diagram.