Q. 54.1( 9 Votes )

# The perimeter of a triangle fields is 540 m, and its sides are in the ratio 25 : 17 : 12. Find the area of the fields. Also, find the cost of ploughing the field at Rs 40 per 100 m^{2}.

Answer :

Given: Ratio of Sides = 25 : 17 : 12

Perimeter = 540 m

Let the sides be,

a = 25x m

b = 17x m

c = 12x m

We know that,

Perimeter of a triangle = a + b + c

⇒ 540 m = 25x m + 17x m + 12x m

⇒ 540 m = 54x m

⇒ x = 10

Therefore,

a = 25x m = 25 × 10 m = 250 m

b = 17x m = 17 × 10 m = 170 m

c = 12x m = 12 × 10 m = 120 m

Now,

We know that,

Area of a scalene triangle = √(s(s-a)(s-b)(s-c))

Where,

⇒ s = 270 m

Now,

Area of a scalene triangle =

√(270m × (270-250)m × (270-170)m × (270-120)m) = √(270m × 20m × 10m × 150cm)

= √81000000 m^{2}

= 9000 m^{2}

Now,

The cost of ploughing 100 m^{2} = Rs 40

Therefore, The cost of ploughing 1 m^{2} = Rs

Therefore, The cost of ploughing 9000 m^{2} = Rs

= Rs 3600

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