1. **State the problem:** We have a rectangular field with width 35 m. Around the field, 15 poles each 5 m wide are placed 7 m apart. We need to find the length of the field. 2. **Understand the setup:** The poles and spaces between them form the perimeter. Total width of poles is $15 \times 5 = 75$ m. 3. **Calculate the perimeter:** The distance between poles is 7 m, and there are 15 poles, so the total perimeter $P$ is given by $$P = 7 \times 15 + 75 = 105 + 75 = 180 \text{ m}.$$ 4. **Use the perimeter formula for a rectangle:** $$P = 2 \times (\text{length} + \text{width})$$ Given width $= 35$ m, substitute values: $$180 = 2 \times (\text{length} + 35)$$ 5. **Solve for length:** $$90 = \text{length} + 35$$ $$\text{length} = 90 - 35 = 55 \text{ m}.$$ **Final answer:** The length of the rectangular field is $55$ meters.