To find the radius of a circle, we need to use the relationship between the chord length and the perpendicular distance from the center.

Given:
Length of the chord (c) = 4 cm
Perpendicular distance from the center (d) = 1.5 cm

Let's consider the following diagram to understand the problem:

```
O
/ \
/ \
/ \
A B
```

In the diagram, O represents the center of the circle, AB represents the chord, and the perpendicular distance from the center O to the chord AB is represented by d.

1. Understanding the relationship between the chord length and the perpendicular distance:
- The perpendicular distance from the center to the chord bisects the chord into two equal parts.
- Therefore, AO = BO = 2 cm (half of the chord length).

2. Using the Pythagorean theorem to find the radius:
- Let's consider the right-angled triangle AOB.
- Applying the Pythagorean theorem: (AO)^2 + (AB/2)^2 = (OB)^2
- Substituting the known values: (2 cm)^2 + (4 cm/2)^2 = (OB)^2
- Simplifying: 4 cm + 4 cm = (OB)^2
- Combining like terms: 8 cm = (OB)^2
- Taking the square root of both sides: √8 cm = OB
- Simplifying: 2√2 cm = OB

Therefore, the radius of the circle is 2√2 cm.

In conclusion, the radius of the circle is 2√2 cm, which is found by using the relationship between the chord length and the perpendicular distance from the center.