Length and breadth of a rectangular field are (x + 7) cm and (x − 6) cm, respectively. If the cost of ploughing the field at a rate of Rs. 6 per cm² is Rs. 3348, then find the cost of fencing the field at a rate of Rs. 16 per
cm.

Let the length = L = x + 7 cm Let the breadth = B = x − 6 cm Use the ploughing cost to find x. Rate of ploughing = Rs. 6 per cm² Total cost = Rs. 3348 Area of the field = Cost / Rate = 3348 / 6 = 558 cm² Area of rectangle = L × B So, (x + 7)(x − 6) = 558 Expand: x² + x − 42 = 558 x² + x − 600 = 0 Solve this quadratic: Discriminant D = 1 + 4 × 600 = 2401 = 49² x = [−1 ± 49] / 2 x₁ = (−1 + 49) / 2 = 48 / 2 = 24 x₂ = (−1 − 49) / 2 = −50 / 2 = −25 (reject, time/length cannot be negative) So x = 24 Then L = x + 7 = 24 + 7 = 31 cm B = x − 6 = 24 − 6 = 18 cm Find the perimeter and fencing cost. Perimeter P = 2(L + B) P = 2(31 + 18) P = 2 × 49 P = 98 cm Rate of fencing = Rs. 16 per cm Cost of fencing = 16 × 98 = 1568 rupees Answer: Rs. 1568