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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

Updated On: Jan 15, 2026
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Solution and Explanation

The area of a rhombus is calculated using the formula: Area = \(\frac{1}{2}\) × d1 × d2, where d1 and d2 represent the lengths of the diagonals.

the diagonals of the rhombus

Given:
The area of the rhombus is 96. Therefore,  \(\frac{1}{2} \times d_1 \times d_2 = 96\). Multiplying both sides by 2 yields \(d_1 \times d_2 = 192\).

The rhombus is inscribed within a circle with a radius of 10 m. The diagonals of a rhombus bisect each other at right angles. This creates a right triangle where the semi-diagonals (\(\frac{d_1}{2}\) and \(\frac{d_2}{2}\)) are the legs and the radius of the circle (10 m) is the hypotenuse. Applying the Pythagorean theorem:

\[ \left( \frac{d_1}{2} \right)^2 + \left( \frac{d_2}{2} \right)^2 = 10^2 = 100 \] Simplifying this equation gives: \[ \frac{d_1^2 + d_2^2}{4} = 100 \Rightarrow d_1^2 + d_2^2 = 400 \]

Using the algebraic identity \((d_1 + d_2)^2 = d_1^2 + d_2^2 + 2d_1 d_2\), we can substitute the known values:

\[ (d_1 + d_2)^2 = 400 + 2(192) = 400 + 384 = 784 \] Taking the square root of both sides gives the sum of the diagonals: \[ d_1 + d_2 = \sqrt{784} = 28 \]

Cost Calculation for Electric Wire along Diagonals:
The total length of the diagonals is \(d_1 + d_2 = 28\) m.
The cost of laying electric wire is ₹125 per meter.
Total Cost = \(28 \times 125 = ₹3500\)

Final Answer: ₹3500

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