The perimeter of a triangular field is 540 m, and its sides are in the

1.	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 m2.
Answer» Perimeter of triangle = 540 m Let the sides of triangle be, a, b and c On dividing 540 m in the ratio 25:17:12, we get a = 25x m b = 17x m c = 12x m We know that, Perimeter of a triangle = Sum of all the sides = a + b + c 540 = 25x + 17x + 12x = 54 x x = 10 Sides are: a = 25x = 250 m b = 17x = 170 m c = 12x = 120 m Let a, b and c be the sides of a triangle. Apply Heron's Formula to find the area of triangle. Area = \(\sqrt{S(S-a)(S-b)(S-c)}\) Where S = \(\frac{a + b + c}{2}\) S = 1/2(250+170+120) = 270 m Area = √(270(270-250)(270-170)(270-120)) = √(270 x 20 x 10 x 150) = 9000 Area of triangle is 9000 m². Now, The cost of ploughing 100 m² = ₹40 The cost of ploughing 1 m² = ₹ 40/100 Therefore, cost of ploughing 9000 m² = 9000 x 40/100 = ₹3600

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 m2.

Answer»

Perimeter of triangle = 540 m

Let the sides of triangle be, a, b and c

On dividing 540 m in the ratio 25:17:12, we get

a = 25x m

b = 17x m

c = 12x m

We know that, Perimeter of a triangle = Sum of all the sides = a + b + c

540 = 25x + 17x + 12x

= 54 x

x = 10

Sides are:

a = 25x = 250 m

b = 17x = 170 m

c = 12x = 120 m

Let a, b and c be the sides of a triangle.

Apply Heron's Formula to find the area of triangle.

Area = \(\sqrt{S(S-a)(S-b)(S-c)}\)

Where S = \(\frac{a + b + c}{2}\)

S = 1/2(250+170+120) = 270 m

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

= √(270 x 20 x 10 x 150)

= 9000

Area of triangle is 9000 m².

Now,

The cost of ploughing 100 m² = ₹40

The cost of ploughing 1 m² = ₹ 40/100

Therefore, cost of ploughing 9000 m² = 9000 x 40/100 = ₹3600