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Question
A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.
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Solution
Let the length and breadth of the rectangular sheep pen be x and y respectively.
From the given information,
x + y + x = 70
2x + y = 70 ...(1)
Also, area = xy = 600
Using (1), we have:
x(70 – 2x) = 600
70x – 2x2 = 600
2x2 – 70x + 600 = 0
x2 – 35x + 300 = 0
x2 – 15x – 20x + 300 = 0
x(x – 15) – 20(x – 15) = 0
(x – 15)(x – 20) = 0
x = 15, 20
If x = 15, then y = 70 – 2x = 70 – 30 = 40
If x = 20, then y = 70 – 2x = 70 – 40 = 30
Thus, the length of the shorter side is 15 m when the longer side is 40 m. The length of the shorter side is 20 m when the longer side is 30 m.
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