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 ₹5m^2

Answer 1

Answer:

take the common ratio as x .

25x+17x+12x= 540

sides will be 250,170,120

then find area by heron's formula

area multiply by 5 will give the required cost

Answer 2

Solution :-

Given :

The perimeter of a triangular field = 540 m

Let the sides are 25x, 17x, 12x.

Perimeter of a triangle = Sum of Three Sides

→ 25x + 17x + 12x = 540

→ 54x = 540

→ x = 10

1st side (a) = - 25x

= 25 × 10

= 250 m

2nd side (b) = 17x

= 17 × 10

= 170 m

3rd side (c) = 12x

= 12 × 10

=120 m

Semi Perimeter = a + b + c / 2

= (250 + 170 + 120) / 2

= 540 / 2

= 270 m

By Heron’s Formula,

Area of the Triangle

= √ S(S - a)(S - b)(S - c)

= √ S(S - 250)(S - 170)(S - 120)

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

= √ 270 × 20 × 100 × 150

= √ 81000000

Area of the Triangle = 9000 m²

Hence, the Area of the Triangle = 9000 m²

Cost of fencing one m² = ₹ 5

Cost of fencing the total field

= 9000 × 5

= ₹ 45000