Discussion
A square farm of side 240 meters has a small rectangular area for barn construction. This barn area has its length 10 meters more than its breadth and its area measures one-eighth the square farm. How much the owner has to spend to build a wall around the barn area at rate of Rs. 1.5 per meter?
Answer: A
Find the barn's area, then its dimensions, then its perimeter.
\[ A_{\text{farm}} = 240^{2} = 57{,}600 \text{ m}^{2} \]
\[ A_{\text{barn}} = \frac{57{,}600}{8} = 7200 \text{ m}^{2} \]
With breadth \( b \) and length \( b + 10 \):
\[ b(b + 10) = 7200 \quad\Longrightarrow\quad b^{2} + 10b - 7200 = 0 \]
\[ b = \frac{-10 + \sqrt{100 + 28800}}{2} = \frac{-10 + 170}{2} = 80 \text{ m} \]
So the barn is 80 m by 90 m.
\[ \text{perimeter} = 2(80 + 90) = 340 \text{ m} \]
\[ \text{cost} = 340 \times 1.5 = \text{Rs. } 510 \]
The wall is priced by length, so the area of 7200 m² is only an intermediate step - pricing it by area would give Rs. 10,800.
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