To find the lengths of BC, BD, and CD, let's analyze the given information step by step.
1. B is between A and D, which means that AB + BD = AD. Since AB is given as 7 cm and AD is given as 32 cm, we can substitute these values into the equation: 7 cm + BD = 32 cm. To find BD, we subtract 7 cm from both sides of the equation: BD = 32 cm - 7 cm = 25 cm.
2. C is between B and D, which means that BC + CD = BD. We know that BD is 25 cm from the previous step. To find BC and CD, we need to solve this equation. However, we don't have enough information to determine the exact values of BC and CD.
To visualize the situation, we can make a sketch with the given information:
```
A ------ B ------ C ------ D
| | |
7cm ?cm 25cm
```
In the sketch, A and D represent the endpoints, while B and C are in between. The lengths of AB, BC, CD, and AD are represented by the corresponding values.
Therefore, we have found that BD is 25 cm, but we cannot determine the values of BC and CD without additional information.