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Question
A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .
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Solution
Area of rectangular garden with sides a and b = 100.
a x b= 100
⇒ a = `100/"b"` .......(i)
also 2a + b =30 (two sides of a and one side of b) ... (ii)
Putting (i) in (ii), we get
`2 xx 100/"b" + "b" = 30`
⇒ b2 - 30b + 200 = 0
⇒ b2 - 20b-10b + 200 = 0
⇒ b (b -20) - 10 (b - 20) = 0
⇒ (b - 10) (b - 20) = 0
⇒ Hence b = 10 or 20. Hence a = 10 or 5
Hence sides are either 5 and 20 m or 10 and 10 m.
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