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 * 40 per 100 m.​

Answer 1

Solution :-

Let's the sides of triangle = 25x , 17x , 12x

Perimeter of triangle = 540 m

⇒ 25x + 17x + 12x = 540

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

Now

• 1st side = 25 × 10 = 250 m

• 2nd side = 17 × 10 = 170 m

• 3rd side = 12 × 10 = 120 m

To find Area of triangle. First we have to find Semi-perimeter of the triangle

★ s = ( a + b + c ) / 2

⇒ s = ( 250 + 170 + 120 ) / 2

⇒ s = 270

Now by using Heron's formula

★ Area = √[ s ( s - a ) ( s - b ) ( s - c ) ]

⇒ Area = √[ 270 ( 270 - 250 ) ( 270 - 170 ) ( 270 - 120 )

⇒ Area = √[ 270 × 20 × 100 × 150 ]

⇒ Area = √81,000,000

⇒ Area = 9,000 m²

____________________________

Cost of 100 m² ploughing = 40 rs

Cost of 1 m² ploughing = 40 / 100 = 0.4 Rs

Cost of 9000 m² ploughing :-

⇒ 0.4 × 9000 = 3600 Rs

Cost of ploughing the field is Rs 3600

Answer 2

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