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 _____.
Answer & explanation
Correct answer: option 1
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