The perimeter of a triangular field is 540 m and its sides are in the ratio `25: 17:12`. Find the area of the triangle. Also, find the cost ploughing the field at `Rs. 18.80` per `10 m^2`

Explanation

Let the sides of the triangle be `25x m, 17x m `and `12x m.`
We know:
Perimeter = Sum of all sides
`540 = 25x + 17x + 12x`
`54x = 540`
` x = 10`
Thus, we obtain the sides of the triangle.
`25 xx 10 = 250 m`
`17xx 10 = 170 m`
`12 xx 10 = 120 m`
Now,
Let: `a=250 m, b =170 m` and `c=120 m`
`∴s= 540/2=270 m`
By Heron's formula, we have:
Area of triangle `= sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(270(270-250)(270-170)(270-120))`
`=sqrt(270xx20xx100xx150)`
`=sqrt(30xx3xx3xx20xx20xx5xx30xx5)`
`=30×3×20×5`
`=9000 m^2`
Cost of ploughing `10 m`field `= Rs 18.80`
Cost of ploughing `1 m` field `= Rs 18.8010`
Cost of ploughing `9000 m` field `= 18.8010xx9000= Rs 16920`