Discussion
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.
Answer: D
The compound wall covers one side, so the wire spans the opposite side and both ends. Let the fenced-opposite side be \( L \) and each end \( W \).
\[ L + 2W = 30, \qquad L \times W = 100 \]
Substituting \( L = 30 - 2W \):
\[ (30 - 2W)W = 100 \quad\Longrightarrow\quad 2W^{2} - 30W + 100 = 0 \]
\[ W^{2} - 15W + 50 = 0 \quad\Longrightarrow\quad (W - 5)(W - 10) = 0 \]
\( W = 5 \) gives \( L = 20 \); \( W = 10 \) gives \( L = 10 \). Only 20 m × 5 m appears among the options.
Checking: \( 20 + 5 + 5 = 30 \) m of wire and \( 20 \times 5 = 100 \) m².
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