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.
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