Question
A farmer has a rectangular field. The length of the
field is 20 meters more than twice its width. The area of the field is 150 square meters. What are the length and width of the field?Solution
Let the width of the field be x meters. Then, the length of the field is 2x + 20 meters. Area of the field = Length * Width 150 = (2x + 20) * x 150 = 2x² + 20x Rearranging the equation: 2x² + 20x - 150 = 0 Dividing through by 2: x² + 10x - 75 = 0 Solving the quadratic equation: x = [-10 ± √(10² - 4 * 1 * -75)] / 2 x = [-10 ± √(100 + 300)] / 2 x = [-10 ± √400] / 2 x = [-10 ± 20] / 2 Taking the positive root: x = (20 - 10) / 2 = 5 meters length = 2*5 + 20 = 30 meter Answer: d) Length = 30 meters, Width = 5 meters
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