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 Rs 5 per $m^2,$

Answer 1

Let the sides of the triangle be 25x m, 17x m and 12x m.
We know:
Perimeter = Sum of all sides
or, 540 = 25x + 17x + 12x
or, 54x = 540
or, x = 10
Thus, we obtain the sides of the triangle.
25×10 = 250 m
17×10 = 170 m
12×10 = 120 m
Now,
Let: a=250 m, b =170 m and c=120 m
∴s= 5402=270 m
By Heron's formula, we have:
Area of triangle = √s(s-a)(s-b)(s-c)
=√270(270-250)(270-170)(270-120)
=√270×20×100×150
=√30×3×3×20×20×5×30×5
=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 = 18.8010×9000= Rs 16920