In \(\bigtriangleup\)XYZ, let's use the Angle Bisector Theorem to find the length of XW.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

In this case, since W is on XZ and XY = 3cm and YZ = 7cm, we have \(\frac{XW}{ZW} = \frac{XY}{YZ} = \frac{3}{7}\). 

Since XZ = 5cm, we can write XW + ZW = 5cm. Substituting ZW = \(\frac{7}{3}\)XW, we get:

 XW + \(\frac{7}{3}\)XW = 5cm.

Solving for XW, we get:

XW = \(\frac{15}{10}\)cm = 1.5cm.