Question
The dimensions of a rectangular field are given as
follows: the length is (x + 4) cm and the breadth is (x – 2) cm. It costs Rs. 8 per square centimeter to plough this field, and the total ploughing expense amounts to Rs. 3456. Calculate the expense of fencing this field at a rate of Rs. 15 per centimeter.Solution
Area of field = 3456/8 = 432 cm2 So, (x + 4)(x – 2) = 432 Or, x2 + 2x – 440 = 0 Or, x2 + 22x – 20x – 440 = 0 Or, x(x + 22) – 20(x + 22) = 0 Or, (x + 22)(x – 20) = 0 So, x = 20 Perimeter of the field = 2 × {(20 + 4) + (20 – 2)} = 84 metres Desired cost = 84 × 15 = Rs. 1260
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