1. **State the problem:** We have a right-angled triangle XYZ with right angle at Z. Point W lies on XY such that WZ is perpendicular to XY, dividing the triangle into WXZ and WZY. Given WX = 4 cm, WZ = 1.6 cm, ZY = 3 cm. We need to calculate: a) Length of WY b) Length of XY (answer to 1 decimal place). 2. **Understand the geometry:** Since WZ is perpendicular to XY, triangles WXZ and WZY are right-angled triangles. 3. **Calculate WY:** Triangle WZY has right angle at Z, sides WZ = 1.6 cm and ZY = 3 cm. Using Pythagoras theorem: $$WY = \sqrt{WZ^2 + ZY^2} = \sqrt{1.6^2 + 3^2} = \sqrt{2.56 + 9} = \sqrt{11.56}$$ $$WY = 3.4\text{ cm (rounded to 1 decimal place)}$$ 4. **Calculate XY:** Since WX = 4 cm and WY = 3.4 cm, XY = WX + WY = 4 + 3.4 = 7.4 cm **Final answers:** a) WY = 3.4 cm b) XY = 7.4 cm