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

GIVEN :

Perimeter of triangular field = 540m

Ratio of the three sides = 25:17:12

Let the ratio be x

Perimeter of traingle = Sum of three sides.

According to the problem,

25x + 17x + 12x = 540

54x = 540

x = 540/54

x = 10

Substitute x

25x = 25(10) = 250

17x = 17(10) = 170

12x = 12(10) = 120

The sides of the triangle are 250, 170, 120.

Area of triangle using Heron's formula

$= \sqrt{(s(s-a)(s-b)(s-c)}$

S = 250 + 170 + 120 / 2

S = 540/2

S = 270

Substitute S in the formula.

$= \sqrt{s(s-a)(s-b)(s-c)} \\ \\ = \sqrt{270(270-250)(270-170)(270-120)} \\ \\ = \sqrt{270(20)(100)(150)} \\ \\ = \sqrt{270(300000)} \\ \\ = \sqrt{81000000} \\ \\ = 9000 {m}^{2}$

Therefore, the area of triangle = 9000m²

Cost of ploughing one m² field = ₹5

Cost of ploughing the total field :

= 9000 × 5

= ₹45000

Therefore, the cost of ploughing total field = ₹45000.

Answer 2

Answer:

rs.45000

Step-by-step explanation:

Given,

perimeter of triangular field = 540m

ratio of the sides = 25:17:12

let, The sides of the triangle are 25x, 17x and 12x

As we know,

Perimeter of triangle = Sum of all sides

Therefore,

25x+17x+12x = 540

54x = 540

x = 10

The first side of the triangle (a)= 25x

a = 25(10)

a = 250

The second side of the triangle (b) = 17x

b = 17(10)

b = 170

The third side of the triangle(c) = 12x

c = 12(10)

c = 120

Now, from heron's formula

$area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ s = \frac{a + b + c}{2} \\ \\ s = \frac{250 + 170 + 120}{2} \\ \\ s = \frac{540}{2} \\ \\ s = 270 \\ \\ \\ now, \\ \\ area \: of \: triangle = \sqrt{270(270 - 250)(270 - 170)(270 - 120)} \\ \\ = \sqrt{270(20)(100)(150)} \\ \\ = \sqrt{81000000cm} \\ \\ = \sqrt{810000m} \\ \\ = 9000m$

_____________________________

To plough 1m^2, it costs rs. 5

cost for ploughing 900m is

= 5 × 9000

= 45000

Therefore,

it costs rs. 45000 to plough tge triangular field!