The perimeter of a triangular field is 540cm and its sides are in the ratio 25:17:12.Find the area of the triangle also.Find the cost of captivating the field at ₹24.60 per 100cm².
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Answer:
Area of the triangle=9000 cm²,
Cost of captivating the field = ₹ 2214
Step-by-step explanation:
The sides are in the ratio 25:17:12
Let x be the common multiple
So, the sides are 25x, 17x and 12x
∴ Perimeter = sum of its sides
540 = 25x+17x+12x = 54x
∴ x = 10
Hence the sides are 250, 170 and 120
Now, the area can be found by using Heron's Formula
A=√[s(s-a)(s-b)(s-c)]
where a, b & c are the three sides
and s=(a+b+c)/2
Now,
a=250
b=170
c=120
s=(250+170+120)/2=540/2=270
A=√[270(270-250)(270-170)(270-120)
=√[270×20×100×150]
=9000 cm²
Area of the triangle=9000 cm²
Cost per 100cm²=24.60
Cost of 9000cm²=24.60×9000/100
=2214
Cost of captivating the field = ₹ 2214
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