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 .............

Let the side of triangular park be 12x, 17x, and 25x.

Perimeter = 1080 m

12x + 17x + 25x = 1080

54x = 1080

x = 20

sides of park-

a  = 12x = 12 $$\times$$ 20 = 240 m

b = 17x = 17 $$\times$$ 20 = 340 m

c = 25x = 25 $$\times$$ 20 = 500 m

area from the Herons formula-

s = $$\frac{a + b + c}{2} = \frac{240 + 340 + 500}{2} = 540$$

Area = $$\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{540(540-240)(540-340)(540-500)}$$

= \sqrt{540 \times 200 \times 300 \times 40} m^2 =  \sqrt{1296000000} m^2 = 36000 m^2$$

= $$\frac{36000}{10000} hectares = 3.6 hectares$$