Question

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

Answer 1

The are of the rhombus is given by,
Area = $\frac{1}{2}$ × d1 × d2
Where d1 & d2 are the diagonals of the rhombus.

Area = $\frac{1}{2}$ × d1 × d2
96 = $\frac{1}{2}$ × d1 × d2
96 × 4 = 2 × d1 × d2

Also,
$(\frac{d_1}{2})^2+(\frac{d_2}{2})^2=10^2$

d12 + d22 = 400
(d1 + d2 )2 = d12 + d22 + 2 × d1 × d2
(d1 + d2 )2 = 400 + 4(96)
(d1 + d2 )2 = 4(100 + 96)
(d1 + d2 )2 = 4(196)
(d1 + d2) = 2(14)
d1 + d2 = 28

The cost of laying electric wires along the diagonals at the rate of per meter ₹125.
= 28 × 125
= ₹3500.