Discussion
The area of a rectangular field is 1008 m2. Its shorter side is \(\frac{1}{8}\) of the sum of its longer side and one of its diagonals. What is the cost of fencing the field at ₹ 24 per m?
Answer: C
The cost of fencing is ₹ 3,792. Let the longer side be \(l\), the shorter side \(b\) and the diagonal \(d\). The condition says \(b = \frac{l + d}{8}\), so \(d = 8b - l\). Squaring and using \(d^{2} = l^{2} + b^{2}\): \[ 64b^{2} - 16bl + l^{2} = l^{2} + b^{2} \] \[ 63b^{2} = 16bl \Rightarrow l = \frac{63b}{16} \] With area \(lb = 1008\): \[ \begin{aligned} \frac{63b^{2}}{16} &= 1008 \Rightarrow b^{2} \\ &= 256,\ b \\ &= 16,\ l \\ &= 63 \end{aligned} \] Perimeter \(= 2(63 + 16) = 158\) m, and \(158\times 24 = 3792\).
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