Q. 54.1( 9 Votes )

The perimeter of a triangle fields is 540 m, and its sides are in the ratio 25 : 17 : 12. Find the area of the fields. Also, find the cost of ploughing the field at Rs 40 per 100 m2.

Answer :

Given: Ratio of Sides = 25 : 17 : 12


Perimeter = 540 m


Let the sides be,


a = 25x m


b = 17x m


c = 12x m



We know that,


Perimeter of a triangle = a + b + c


540 m = 25x m + 17x m + 12x m


540 m = 54x m



x = 10


Therefore,


a = 25x m = 25 × 10 m = 250 m


b = 17x m = 17 × 10 m = 170 m


c = 12x m = 12 × 10 m = 120 m


Now,


We know that,


Area of a scalene triangle = √(s(s-a)(s-b)(s-c))


Where,




s = 270 m


Now,


Area of a scalene triangle =


√(270m × (270-250)m × (270-170)m × (270-120)m) = √(270m × 20m × 10m × 150cm)


= √81000000 m2


= 9000 m2


Now,


The cost of ploughing 100 m2 = Rs 40


Therefore, The cost of ploughing 1 m2 = Rs


Therefore, The cost of ploughing 9000 m2 = Rs


= Rs 3600


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