The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of a triangle.
Answers
Given : The perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17: 12
Let the sides be a = 25x , b = 17x and c = 12x .
Perimeter of ∆ = a + b + c
⇒ 540 = 25x + 17x + 12x
⇒ 54x = 540
⇒ x = 540/54
⇒ x = 10
So the Sides of a triangle are :
a = 25x = 25 × 10 = 250 m
b = 17x = 17 × 10 = 170 m
c = 12x = 12 × 10 = 120 m
Semi Perimeter of the ∆,s = (a + b + c) /2
Semi-perimeter (s) = (250 + 170 + 120)/2
s = 540/2
s = 270 m
Using Heron’s formula :
Area of the wall , A = √s (s - a) (s - b) (s - c)
A = √270(270 - 250)(270 - 170)(270 - 120)
A = √270 × (20) × (100) × (150)
A = √(9 × 3 × 10) × (2 × 10) × (10 × 10) × (10 × 15)
A = √(10 × 10 × 10 × 10) × 10 × (9) × (3) × (2) × (3 × 5)
A = √(10 × 10 × 10 × 10) × (2 × 5) × (9) × (3) × (2) × (3 × 5)
A = √(10 × 10 × 10 × 10) × (2 × 2) × (3 × 3) × (3 × 3) × (5 × 5)
A = 10 × 10 × 2 × 3 × 3 × 5
A = 100 × 90
A = 9000 m²
Hence, the area of triangle is 9000 m²
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Answer:
Step-by-step explanation:
Given :-
Perimeter of triangular field = 540 m
Ratio of sides = 25 : 17 : 12.
To Find :-
Area of a triangle.
Formula to be used :-
Area of the triangle = √s(s - a)(s - b)(s - c)
Solution :-
⇒ 25x + 17x + 12x = 540 m
⇒ 54x = 540 m
⇒ x = 540/54
⇒ x = 10 m
The sides of a triangle are a = 250 m b = 170 m c = 120 m and s = 270 m
⇒ Area of the triangle = √s(s - a)(s - b)(s - c)
⇒ Area of the triangle = √ S(S - 250)(S - 170)(S - 120)
⇒ Area of the triangle = √ 270(270 - 250)(270 - 170)(270 - 120)
⇒ Area of the triangle = √ 270× 20×100×150
⇒ Area of the triangle = √ 81000000
⇒ Area of the triangle = 9000 m²
Hence, the area of a triangle is 9000 m².