1. **State the problem:** Linda runs along the path A to B to D to C to A around a rectangular field. We need to find the total distance she runs. 2. **Identify the sides of the rectangle:** Given the rectangle with vertices C, B, D, A: - Side CB = 40 m (top side) - Side BA = 30 m (right side) 3. **Find the lengths of other sides:** - Since it's a rectangle, opposite sides are equal: - Side AD = CB = 40 m - Side DC = BA = 30 m 4. **Calculate the distances for each segment Linda runs:** - Segment A to B: length AB = 30 m (right side) - Segment B to D: B to D is diagonal across the rectangle, so use the distance formula: $$BD = \sqrt{(CB)^2 + (BA)^2} = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50$$ m - Segment D to C: length DC = 30 m - Segment C to A: C to A is diagonal across the rectangle, same as BD, so 50 m 5. **Sum all distances:** $$\text{Total distance} = AB + BD + DC + CA = 30 + 50 + 30 + 50 = 160$$ m 6. **Answer:** Linda runs 160 meters in total.