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
Answers
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
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