A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is
Explanation:
Side of the rhombus = ¼ × 40 = 10 cm.
Area of a rhombus = ½ d1d2 = 96 [d1 and d2 are the two diagonals]
⇒ d1d2 = 192
We know, (d1/2)2 + (d2/2)2 = 102
⇒ d12 + d22 = 400
⇒ (d1 + d2)2 - 2d1d2 = 400
⇒ (d1 + d2)2 – 2 × 192 = 400
⇒ (d1 + d2)2 = 784
⇒ d1 + d2 = 28
Hence, the cost of laying electric wore along its two diagonals = 125 × (d1 + d2) = 125 × 28 = Rs. 3,500
Hence, 3500.
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