1. The problem states that triangle ABC is similar to triangle XYZ, and we know the side length XZ = 10 units. 2. Given triangle ABC has sides AB = 9, BC = 12, and hypotenuse AC = 15, and triangle XYZ is similar, the corresponding sides are proportional. 3. The concept to use here is **proportionality** because similarity of triangles means their corresponding sides are in proportion. 4. To find the area of triangle XYZ, we first find the scale factor between the triangles using corresponding sides. 5. The scale factor $k$ is given by $$k = \frac{XZ}{AC} = \frac{10}{15} = \frac{2}{3}.$$ 6. Since areas scale by the square of the scale factor, the area of XYZ is $$Area_{XYZ} = k^2 \times Area_{ABC} = \left(\frac{2}{3}\right)^2 \times Area_{ABC} = \frac{4}{9} \times Area_{ABC}.$$ 7. Calculate the area of triangle ABC using the right triangle formula: $$Area_{ABC} = \frac{1}{2} \times AB \times BC = \frac{1}{2} \times 9 \times 12 = 54.$$ 8. Substitute to find the area of XYZ: $$Area_{XYZ} = \frac{4}{9} \times 54 = 24.$$ 9. Therefore, the most appropriate concept to use is **proportionality** (option B) to solve for the area of triangle XYZ.