A triangular park in a city has dimensions 100m X 90m X110m.A contract is given to a company for planting grass in the park at the rate of Rs.4000 per hectare.Find the amount to be paid to the company.(Take $\sqrt{2} = 1.414$ )

Rs.

4532.90

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Rs.

4242

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Rs.

1696.80

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Rs.

1000

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Solution

The correct option is C Rs. $1696.80$
$H e r o n^{'} s F o r m u l a :$
Area of a triangle = $Δ = \sqrt{s (s - a) (s - b) (s - c)}$
where $s$ is the semi-perimeter and $a, b$ and $c$ are the sides of the triangle.
$s = \frac{a + b + c}{2}$

Here, for the triangular park,
$a = 100 m, b = 90 m, c = 110 m$ and

$s = \frac{100 + 90 + 110}{2} = 150 m$

Area of the triangular park = $Δ = \sqrt{150 \times 50 \times 60 \times 40} = 3000 \sqrt{2} m^{2} = 0.3 \sqrt{2} h a = 0.4242 h a$

Rate of planting grass = $R s . 4000 / h a$

So, the amount to be paid = $4000 \times 0.4242 = R s . 1696.80$ . $[C]$

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A triangular park in a city has dimensions 100m X 90m X110m.A contract is given to a company for planting grass in the park at the rate of Rs.4000 per hectare.Find the amount to be paid to the company.(Take √2=1.414)

A triangular park in a city has dimensions 100m X 90m X110m.A contract is given to a company for planting grass in the park at the rate of Rs.4000 per hectare.Find the amount to be paid to the company.(Take $\sqrt{2} = 1.414$ )