Question

the perimeter of a triangular field is 540m and its sides are in the ratio 25:17:12.Find the area of the triangle. also find the cost of ploughing the field at Rs18. 80 per 10 m2​

Answer 1

Given

Perimeter of triangular field =540m

Ratio.of sides =25:17:12

cost of ploughing =80 per 10m²

To Find

Cost of ploughing the field

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Sides of triangle be 25x,17x & 12x respectively.

we know that perimeter of triangle is :

S=a+b+c

540=25x+17x+12x

540=54x

x=10

Sides are 25x ,17x & 12x

Sides =25×10,17×10 & 12×10

Therefore ,the sides are: 250m ,170m& 120m

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

By applying Heron's formula we will find the area of triangle

S=a+b+c/2

S=250+170+120/2

S=540/2=270m

Now, finding area:

Area of Triangle =√S(S-a)+(S-b)+(S-c)

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

Area of Triangle=√270×20×100×150

Area of Triangle=9000m²

Given cost of fencing 80 per 10 m²

cost of fencing per m²=80/10=8

Cost of fencing 9000m²=9000×8=₹72000

Cost of fencing @18 if per metre then =9000×18

=₹162000