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 _____.

3.6

We have,

Ratio of sides of the triangle = 12x : 17x : 25x

Perimeter of the triangle = 1080

According to the question

12x + 17x + 25x = 1080

54x = 1080

x = 20

Side of the triangle are = 12 × 20 = 240

= 17 × 20 = 340

= 25 × 20 = 500

Semi perimeter = \(\frac{(240 + 340 + 500) }{2}\) = 540

Area = \(\sqrt {s(s-a)(s-b)(s-c) }\)

= \(\sqrt {540 (540-240)( 540-340)( 540-500) }\)

= \(\sqrt {540 (300)( 200)( 40) }\)

= 36000 m²

= \(\frac{36000 }{10000}\) = 3.6 hectare