1. **Problem Statement:** We have a rectangular field with perimeter 70 m. Its length is 15 m longer than its breadth. The field is surrounded by a concrete path with widths 5 m (top) and 2.5 m (left). We need to find the area of the path. 2. **Define variables:** Let the breadth be $b$ meters. Then the length is $l = b + 15$ meters. 3. **Use perimeter formula:** Perimeter $P$ of a rectangle is given by: $$P = 2(l + b)$$ Given $P = 70$, substitute: $$70 = 2(b + 15 + b) = 2(2b + 15) = 4b + 30$$ 4. **Solve for breadth $b$:** $$4b + 30 = 70$$ $$4b = 70 - 30 = 40$$ $$b = \frac{40}{4} = 10$$ meters 5. **Find length $l$:** $$l = b + 15 = 10 + 15 = 25$$ meters 6. **Dimensions of the field:** Length = 25 m, Breadth = 10 m 7. **Dimensions including the path:** The path adds 5 m on top and 2.5 m on left side. Assuming the path surrounds the field on all sides with these widths, the total length and breadth including the path are: - Total length = field length + 2 * path width on length sides = $25 + 2 \times 5 = 25 + 10 = 35$ m - Total breadth = field breadth + 2 * path width on breadth sides = $10 + 2 \times 2.5 = 10 + 5 = 15$ m 8. **Calculate areas:** - Area of field = $l \times b = 25 \times 10 = 250$ m$^2$ - Area of field + path = total length $\times$ total breadth = $35 \times 15 = 525$ m$^2$ 9. **Area of the path:** $$\text{Area of path} = \text{Area of field + path} - \text{Area of field} = 525 - 250 = 275$$ m$^2$ **Final answer:** The area of the concrete path is **275 square meters**.