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Question
The perimeter of a triangular field is 240m, and its sides are in the ratio 25:17:12. Find the area of the field. Also, find the cost of ploughing the field at ₹ 40 per `m^2`
Solution
Let the sides of the triangular field be 25x, 17x and 12x. As, perimeter = 540 m
⇒ `25x+17x+12x=540`
⇒` 54x=540`
⇒`x=540/54`
⇒`x=10`
So, the sides are 250 m, 170 m and 120 m.
Now, semi-perimeter, `s= (250+170+120)/2=540/2=270m`
So, area of the filed= `sqrt(270(270-250)(270-170)(270-120))`
=`sqrt(270xx20xx100xx150)`
=`sqrt(3^2xx10xx2xx10xx10^2xx3xx5xx10)`
=`3^2xx10^3`
=`9000m^2`
Also, the cost of ploughing the field=`(9000xx40)/100=3600`
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