1. **Stating the problem:** We have a right triangle ABC with right angle at C, where AC = 5.4 m, and a rectangle BCDE attached such that BC is perpendicular to AC and DE is parallel to AC. The vertical side DE measures 2 m, and EF = 1.2 m is a segment on the vertical side parallel to BC. We need to find the length of the segment FD. 2. **Understanding the figure:** - Triangle ABC is right angled at C. - AC = 5.4 m (horizontal side). - BC is perpendicular to AC. - Rectangle BCDE has sides BC and DE vertical, DE = 2 m. - EF = 1.2 m is a segment on the vertical side DE parallel to BC. - Points E and F lie on the vertical side DE. 3. **Analyzing the rectangle BCDE:** Since BCDE is a rectangle, BC = DE = 2 m (vertical sides), and CD = BE = length parallel to AC. 4. **Finding BC:** Since BC is vertical and DE = 2 m, BC = 2 m. 5. **Finding BD:** BD = BC + CD = 2 m + 1.2 m = 3.2 m. 6. **Finding FD:** EF = 1.2 m is part of DE (vertical side), so FD = DE - EF = 2 m - 1.2 m = 0.8 m. **Final answer:** $$FD = 0.8\ \text{m}$$