Finding Unknown Side in Triangle Using Area Relations

In triangle XYZ, the sides measure as follows: side XY is 8 cm, side YZ is 15 cm, and side XZ is unknown. When a line is drawn from point X to point Z, it creates two triangles, XWY and YXZ. If the area of triangle XYZ is equal to the area of triangle XWY, and the area of triangle XYZ is calculated using Heron's formula, can you determine the length of side XZ?

The semi-perimeter $s$ of triangle XYZ can be found using the formula $s = \f\frac{XY + YZ + XZ}{2}$. With the known values, you can set up the computation for the area and solve for XZ using the provided conditions.