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The perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17: 12. The cost of ploughing the field at Rs. 18.80 per $10 m 2$ is Rs. ____.

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Detailed Solution

The perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17: 12. The cost of ploughing the field at Rs. 18.80 per

10 m 2

is Rs. 16920.
Given the perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17: 12.
Let a = 25x, b = 17x, c = 12x.
The perimeter of triangular field = sum of all sides.

⇒ 25 x + 17 x + 12 x = 540 ⇒ 54 x = 540 ⇒ x = 10

Length of side a is,

a = 25 × 10 ⇒ a = 250 c m

Length of side b is,

b = 17 × 10 ⇒ b = 170 c m

Length of side c is,

c = 12 × 10 ⇒ c = 120 c m

The value of s is,

s = p e r i m e t e r 2 ⇒ s = 5402 ⇒ s = 270

Now, using Heron’s formula,

A = s (s − a) (s − b) (s − c)

⇒ A = 270 (270 − 250) (270 − 170) (270 − 120) ⇒ A = 270 × 20 × 100 × 150 ⇒ A = 81000000 ⇒ A = 9000 m 2

Now, the total cost of ploughing is,

Cost = 900010 × 18.80

⇒ Cost = R s .16920

The cost is Rs.16920.

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