the perimeter of a triangular field is 240m and its sides are in the ratio of 3:4:5. find the area of the triangle. Also find the cost of ploughing the field at rs.15 per m^2.
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Answers
Answer:
GIVEN :-
The perimeter of a triangular field is 240 m.
Ratio of sides of triangular field are 3:4:5.
TO FIND :-
The area of the triangular field.
Cost of ploughing.
SOLUTION :-
Let the ratio constant be "x".
✮ Sides of Triangular Field,
➳ a = 3x.
➳ b = 4x.
➳ c = 5x.
✮ Semi - Perimeter of Triangular Field,
➳ Semi - Perimeter = perimeter/2
➳ Semi - Perimeter = 240/2
➳ Semi - Perimeter = 120 m.
✮ Sides of Triangular Field,
As we know that the semi perimeter of a triangle is given by,
➵ Semi - perimeter (a + b + c)/2
➵ 120 m = (3x + 4x + 5x)/2
➵ 120 = 12x/2
➵ (120 × 2)/12 = x
➵ x = 20.
Now substitute the value of x in the sides of triangle,
➳ a = 3x = 60 m.
➳ b = 4x = 80 m.
➳ c = 5x = 100 m.
✮ Area of triangular field,
As we know that the area of triangle is given by,
✯ Area ∆ = √{s(s - a)(s - b)(s - c)}
➟ Area ∆ = √{120(120 - 60)(120 - 80)(120 - 100)}
➟ Area ∆ = √{120 × 60 × 40 × 20}
➟ Area ∆ = √5760000
➟ Area ∆ = 2400 m².
✮ Cost of pluoghing the field,
➳ Cost = Area × Rate.
➳ cost = 2400 × 15
➳ cost = Rs. 36000.
Given, perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8.
Let sides of a triangular field be a = 6x, b = 7x and c = 8x.
Perimeter of a triangular field, 2s = a + b + c ⇒ 420 = 6x + 7x + 8x ⇒ 420 = 21x
⇒ x = 420/21 = 20 m
