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 .

Answer 1

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.