Question : The sides of a triangular park are in the ratio of 12 : 17 : 25 and its perimeter is 1080 m. The area (in hectares) of the park is _______.
Option 1: 3.6
Option 2: 4.2
Option 3: 4.5
Option 4: 4.8
Correct Answer: 3.6
Solution :
Given:
Ratio of sides of the triangle = 12 : 17 : 25
The perimeter of the triangle = 1080
Let the sides of the triangle be $12x$, $17x$, and $25x$.
Perimeter of the triangle $=12x + 17x + 25x = 1080$
$\Rightarrow 54x = 1080$
$\Rightarrow x = \frac{1080}{54} = 20$
Now, the sides are 240, 340, and 500
Semiperimeter (S) = $\frac{240 + 340 + 500}{2} = \frac{1080}{2} = 540$
Area of the triangle = $\sqrt{[s(s - a)(s -b)(s - c)]}$
= $\sqrt{[540(540 - 240)(540 -340)(540 - 500)]}$
= $\sqrt{[540\times 300 \times 200\times 40]}$
= $36000$ m
2
= $3.6$ hectares
Hence, the correct answer is 3.6.
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