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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 triangle. Also, find the cost of ploughing the field at Rs 18.80 per 10 m2.

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Solution

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 ms= 5402=270 mBy 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 m2

Cost of ploughing 10 m2 field = Rs 18.80
Cost of ploughing 1 m2 field = Rs 18.8010

Cost of ploughing 9000 m2 field = 18.8010×9000= Rs 16920

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