1. **State the problem:** We have a rectangular frame made from metal pieces with side lengths 12 m and 5 m. We need to find the total weight of the metal in the frame. 2. **Identify the pieces:** The frame consists of 5 straight pieces: 4 sides of the rectangle and 1 diagonal. 3. **Calculate the perimeter:** The perimeter is the sum of all four sides: $$\text{Perimeter} = 2 \times (12 + 5) = 2 \times 17 = 34 \text{ m}$$ 4. **Calculate the diagonal length:** Use the Pythagorean theorem: $$\text{Diagonal} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ m}$$ 5. **Calculate total length of metal:** Total length is perimeter plus diagonal: $$34 + 13 = 47 \text{ m}$$ 6. **Calculate total weight:** Weight per metre is 1.5 kg, so total weight is: $$1.5 \times 47 = 70.5 \text{ kg}$$ **Final answer:** The total weight of the metal in the frame is **70.5 kg**.