A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

A. $5 m * 5 m$

B. $10 m * 5 m$

C. $15 m * 5 m$

D. $20 m * 5 m$

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Correct Answer : D.

From the question, 2b+l = 30
=> l = 30-2b

A r e a = 100 m^{2} \Rightarrow l \times b = 100 \Rightarrow b (30 - 2 b) = 100 b^{2} - 15 b + 50 = 0 \Rightarrow (b - 10) (b - 5) = 0

b = 10 or b = 5
when b = 10 then l = 10
when b = 5 then l = 20
Since the garden is rectangular so we will take value of breadth 5.
So its dimensions are 20 m * 5 m

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