A farmer has 70m 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 600sq.m , find the length of its shorter side.

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Solution

Let the length and breadth of the sheep pen be 'l' and 'b'.
Length of fencing three sides of the sheep pen = l + 2b = 70
Area of the sheep pen = l x b = 600
⇒ l = 600/b
⇒ 600/b + 2b = 70
⇒ 2b² - 70b + 600 = 0
⇒ b² - 35b + 300 = 0
⇒ (b - 15)(b - 20) = 0
⇒ b = 15 or 20.
⇒ l = 40 or 30
Therefore, the shorter side of the sheep pen = 15 or 20.

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