Question

The perimeter of a triangular field is 540 m, 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 100 m².

Answer 1

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`